Review Article Dynamic Responses and Vibration Control of ...downloads.hindawi.com/journals/tswj/2014/538457.pdfReview Article Dynamic Responses and Vibration Control of the Transmission

Review ArticleDynamic Responses and Vibration Control of the TransmissionTower-Line System A State-of-the-Art Review

Bo Chen1 Wei-hua Guo1 Peng-yun Li2 and Wen-ping Xie2

1 Key Laboratory of Roadway Bridge and Structural Engineering Wuhan University of Technology PO Box 219No 122 Luoshi Road Wuhan 430070 China

2Guangdong Power Grid Corporation Co Ltd Guangzhou 510080 China

Correspondence should be addressed to Bo Chen cbsteven163com

Received 18 April 2014 Accepted 19 May 2014 Published 3 July 2014

Academic Editor Ting-Hua Yi

Copyright copy 2014 Bo Chen et alThis is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This paper presented an overview on the dynamic analysis and control of the transmission tower-line system in the past fortyyears The challenges and future developing trends in the dynamic analysis and mitigation of the transmission tower-line systemunder dynamic excitations are also put forward It also reviews the analytical models and approaches of the transmission towertransmission lines and transmission tower-line systems respectively which contain the theoretical model finite element (FE)model and the equivalent model shows the advances in wind responses of the transmission tower-line system which containsthe dynamic effects under common wind loading tornado downburst and typhoon and discusses the dynamic responses underearthquake and ice loads respectivelyThe vibration control of the transmission tower-line system is also reviewed which includesthe magnetorheological dampers friction dampers tuned mass dampers and pounding tuned mass dampers

1 Introduction

The degradation of civil engineering structures due to harshenvironment may lead to structural damage and failureassociated with the events such as member fracture columnbuckling and brace breakage [1 2] To be a kind of high-rise structure with small damping overhead transmissiontower-line systems are critical infrastructure for electricalpower transmission and are used throughout the world [3]Transmission tower-line systems are prone to the dynamicexcitation such as wind earthquake and iced shedding Assupporting structures of coupled tower-line systems trans-mission towers have relatively complex structural geometriesand present obvious nonlinear vibration associated withflexibility of transmission lines In reality there exists a stronginteraction between the motion of the truss tower and that ofthe transmission lines subjected to dynamic loading each ofwhich has frequency-dependent stiffness properties leadingto rather complex dynamic behaviour [4ndash6]The failure of thetowers under dynamic loading has been documented inmanyliteratures [7 8]Therefore it is relevant to assess the dynamic

performance of transmission tower-line systems consideringboth elastic and inelastic responses

The interest in the ability to monitor and mitigate thedynamic responses of the transmission tower-line systemis pervasive throughout the civil and electrical engineeringcommunities To examine the properties of the coupledtransmission tower-line system many theoretical and exper-imental investigations have been carried out during the pasttwo decades With regard to the approaches and techniquesused for performance evaluation and disaster mitigationthey can be classified into two major categories one isthe conventional approach without considering nonlineartower-line interaction and the other is the approach basedon coupled tower-line system Conventionally transmissiontower-line systems can be designed and constructed usingappropriate design standards [9ndash11] The suggested designloads are commonly calibrated based on the assumptionthat the tower behaves elastically during dynamic excitationIn addition the dynamic interaction between the towerand transmission lines cannot be taken into considerationduring the common design process Therefore this design

Hindawi Publishing Corporatione Scientific World JournalVolume 2014 Article ID 538457 20 pageshttpdxdoiorg1011552014538457

2 The Scientific World Journal

approach does not provide deep insights into inelastic andnonlinear tower behaviour under strong dynamic excitationseven though the consideration of inelastic responses canbe important [12] Furthermore the primary environmentalload considered in the design of transmission structures isthe wind load although the ice load may govern the designof transmission tower-line systems in some cold regionsTherefore the damage and failure of transmission tower-linesystems have been frequently reported across the world eventhough the towers are designed and constructed strictly basedon the specifications and codes

After that the development and application of struc-tural assessment and mitigation approaches for transmissiontower-line systems in the fields of civil and electrical engi-neering have attracted more and more attention To over-come the shortcomings of conventional approaches manyanalytical models and approaches have been proposed anddeveloped for transmission tower-line systems in recent yearswith the aid of various techniques such as wind engineeringearthquake engineering structural health monitoring andvibration control However there are still many challengesand difficulties in the performance evaluation and vibrationcontrol techniques for the practical application of trans-mission tower-line system in various service conditionsTherefore it is still essential to investigate the feasibilityvalidity and applicability of the performance assessment andcontrol approaches of the transmission tower-line systems

This paper reviews the dynamic responses and control ofthe transmission tower-line system in the last two decadesThe challenges and future trends in the disaster monitor-ing and mitigation of the transmission tower-line systemsubjected to dynamic excitations are also put forward Thestructure of the rest of the paper is as follows Section 2reviews the analytical models of transmission lines trusstowers and the coupled tower-line system which containsthe theoretical model finite element (FE) model and theequivalent model Section 3 reviews the wind responsesof the transmission tower-line system which contains thestructural performance subjected to various wind loadingssuch as common winds tornado downburst and typhoonrespectively and the experiment and field testing on windeffects Sections 4 and 5 discuss the seismic responses andice-induced responses of the transmission tower-line systemrespectively The vibration control of the transmission tower-line system is also reviewed Finally the challenges andfuture trends in the dynamic assessment and mitigationof transmission tower-line system are summarized in theconclusions

2 Model of Transmission Tower-Line System

21 Model of Transmission Line

(1) Theoretical Model To examine the properties of a coupledtransmission tower-line system many analytical models aredeveloped and presented during the past two decades [13ndash16] Irvine [13] systematically investigated the cable vibrationthrough theoretical deduction and corresponding results arecommonly taken as the benchmark to assess the effectiveness

of various numerical simulating approaches Based on theconclusions provided by Irvine [13] the natural frequenciesof a transmission line for antisymmetric in-plane vibration120596119904can be expressed as

120596119904=

2119899120587

119897

radic119867

119898

(119899 = 1 2 3 ) (1)

The natural frequencies of a transmission line for the sym-metric in-plane vibration can be determined by solving thefollowing equations

119905119892

120578

2

=

120578

2

minus

4

1205822(

120578

2

)

2

120578 =

120596119904119897

radic119867119898

1205822

=

(119898119892119897)2

1198673

119864119860 (2)

where 119867 is the tensile force of a transmission line 119898 is themass of a transmission line per meter 119864 and119860 are the Youngmodulus and sectional area of a transmission line 119897 is thehorizontal span of a transmission line In addition the naturalfrequencies of a cable for out-of-plane vibration 120596V are

120596V =119899120587

119897

radic119867

119898

(119899 = 1 2 3 ) (3)

(2) FE Model A transmission line can be modelled by usingcable elements in the FE method [17ndash19] The equilibriumequation of the 119894th cable element can be established by usingthe virtual work principle based on the nonlinear FEmethodThe strainmatrix of the 119894th cable elementB(119894) is the sumof thelinear strain matrix B(119894)

119871and the nonlinear strain matrix B(119894)NL

B(119894) = B(119894)119871

+ B(119894)NL (4)

Both the linear strain matrix B(119894)119871

and the nonlinear strainmatrix B(119894)NL relate to the shape function of a certain cableelement The stiffness matrix of the 119894th cable element K(119894) inthe global coordinate system (GCS) can be expressed as thesum of the elastic stiffness matrix K(119894)

119890 displacement stiffness

matrix K(119894)119892 and the stress stiffness matrix K(119894)

120590 Consider

K(119894) = K(119894)119890

+ K(119894)119892

+ K(119894)120590 (5)

The elastic stiffness matrix K(119894)119890

can be constructed only bythe linear strain matrix B(119894)

119871 while the displacement stiffness

matrixK(119894)119892can be constructed by both the linear strainmatrix

B(119894)119871

and nonlinear strain matrix B(119894)NL The stress stiffnessmatrix K(119894)

120590is constructed by using the shape function of

the cable element and the element stress 120590 The globalstiffness matrix of a transmission line can be determined bycombining all the element stiffness matrices in the GCS

K119897=

119899119897

sum

119894=1

K(119894) (6)

where 119899119897 denotes the number of all the cable elements in atransmission line The mass matrix of the transmission line

The Scientific World Journal 3

l l

v

u

ll l ll

12057911205792

1205793 1205794 1205795

1205796

1205797h7

h6h5

h1h2

h3

(a)

m1

m2

m3

L1

L2

L3

(b)

Figure 1 MDOF elastic model of a transmission line (a) In-plane vibration (b) Out-of-plane vibration

in the GCS can be expressed by using lumped mass matrix orconsistent mass matrix based on the FE method Consider

M119897=

119899119897

sum

119894=1

M(119894) (7)

(3) MDOF Equivalent Model The transmission line can besimulated as several lumped masses connected with elasticelements as shown in Figure 1 which is theMDOF equivalentmodel The Hamilton variational statement of dynamicsindicates that the sum of the time variations of the differencein kinetic and potential energies and the work done by thenonconservative forces over any time interval 119905

1to 1199052equals

zero [19]The application of this principle can lead directly tothe equation of motion of a transmission line

int

1199052

1199051

120575 [119879line (119905) minus 119880line (119905)] 119889119905 + int

1199052

1199051

120575119882line (119905) 119889119905 = 0 (8)

in which 119879(119905) and 119880(119905) are the kinetic energy and potentialenergy of a transmission line119882line(119905) equals the virtual workdone by the nonconservative forces on a transmission lineIt is clear that the transmission line may vibrate around itsbalanceable position when it is subjected to the externaldisturbance The generalized coordinate 119902

119894of a transmission

line namely 120585 and 120575 can be defined as the difference of theangle 120579 and length 119897 respectively as follows

120585119894= 120575120579119894= 120579119894minus 1205791198940

120575119894= 120575119897119894= 119897119894minus 1198971198940minus 119897119894119904

(9)

where 1205791198940is the original value of 120579

119894for the 119894th element 119897

1198940and

119897119894are the original length and current length of the 119894th element

respectively and 119897119894119904is the static deformation due to the gravity

of the 119894th elementThe equation of motion of an N-DOF transmission line

can be derived directly from theHamilton equation by simplyexpressing the total kinetic energy 119879line the total potentialenergy 119880line and the total virtual work 119882line in terms of aset of generalized coordinates 119902

119894 namely 120585 and 120575 Then

introducing the expression into the Hamilton equation andcompleting the variation of the first term yield the Lagrangeequations of a transmission line as follows

119889

119889119905

(

120597119879line120597 119902119894

) minus

120597119879line120597119902119894

+

120597119880line120597119902119894

= 119876119894 (10)

where 119876119894is the generalized forcing function of the transmis-

sion line corresponding to the generalized coordinates 119902119894

After establishing the kinetic energy and potential energyof transmission line the mass and stiffness matrices canbe determined through partial differential calculation of thegeneralized velocity and generalized displacement respec-tivelyThemass matrix of a transmission line for the in-planevibrationMin

119897can be deduced by computing partial differen-

tial of the derivative of generalized coordinates 120597119879120597

120585119894and

120597119879120597

120575119894 respectively The stiffness matrix of a transmission

line for the in-plane vibration Kin119897

can be determined bycomputing partial differential of the generalized coordinates120597119880120597120585

119894and 120597119880120597120575

119894 respectively In addition the transmis-

sion line can be simplified as a hanging linewith a few lumpedmasses when considering the out-of-plane vibration Themass matrix Mout

119897and stiffness matrix Kout

119897of transmission

line can be deduced in the same way

22 Model of Transmission Tower

(1) FE Model The transmission tower is a typical spatialstructure constructed by using steel members which can bemodelled by using beam and truss elements based on the FEmethod The element stiffness matrix K(119898) and mass matrixM(119898) of the 119898th element in the GCS can be determinedby transforming the element stiffness matrix K(119898)

119890and mass

matrixM(119898)119890

in the local coordinate system (LCS) with the aidof coordinate transformation matrix T(119898)

119886

K(119898) = T(119898)119879119886

K(119898)119890

T(119898)119886

M(119898) = T(119898)119879119886

M(119898)119890

T(119898)119886

(11)

After determining the element stiffness and mass matricesunder the GCS one can construct the position matrixof element freedom T(119898)

119888following the FEM connection

information of each element under both local and globalcoordinate systems Thus the global stiffness matrix K

119905and

mass matrix M119905of a transmission tower in the GCS can be

expressed as

K119905=

119899119890

sum

119898=1

T(119898)119879K(119898)T(119898)

M119905=

119899119890

sum

119898=1

T(119898)119879M(119898)T(119898)(12)


(a)

15000

29500

55500

43000

98000

76500

66500

88500

122000

110000

(b)

Figure 2 Analytical model of a transmission tower (a) 3D FE mode (b) 2D model

where 119899119890 is the total element number of the finite elementmodel of a transmission tower and T(119898) is the freedomtransform matrix from element coordinate system to theGCS which is the product of coordinate transformationmatrix T(119898)

119886and position matrix T(119898)

119888of the119898th element

(2) 2D Lumped Mass Model If a 3D finite element dynamicmodel is used to model a tower with many transmissionlines the numerical step-by-step integration in the timedomain to determine dynamic responses of the tower-linecoupled system will be very time-consuming which makesit impractical for parametric study and vibration controlinvestigation The dynamic excitation on the tower such aswind loads and earthquakes can usually be modeled as astationary or nonstationary stochastic process in time andnonhomogeneous in spaceThedigital simulation of dynamicloading of a 3D finite element model of the transmissiontower-line system with the aid of the spectral representationmethod [20 21] may need enormous computation effort Tothis end a 2D lumpedmassmodel is commonly used in prac-tice to investigate the windearthquake-induced dynamicresponse of a complicated transmission tower-line system[22] (see Figure 2)

When a 3D FE dynamic model of a transmission toweris reduced to a 2D lumped mass model some assumptionsare commonly adopted Firstly the mass of the transmissiontower including the masses of all structural components andall nonstructural components and all equipment in the toweris concentrated at several floors onlyThen the average of thedisplacements of all nodes at a given floor in one commondirection is defined as the nominal displacement of that floorin that direction Finally only the horizontal dynamic loadingand responses are considered

With these assumptions the number of dynamic degreesof freedom of a transmission tower in the lumped massmodel is the number of floors selected The mass matrix

M119905of the lumped mass model is a diagonal matrix The

stiffness matrix K119905of the lumped mass model of 119899 degrees

of freedom can be obtained based on the 3D FE model of thetransmission tower by taking the following steps (1) apply thesame horizontal force at each node at the 119894th floor such thatthe sum of all forces equals 1 (2) determine the horizontaldisplacement of each node at the 119895th floor and define thenominal displacement of the 119895th floor to have the flexibilitycoefficient 119889

119895119894(119894 119895 = 1 2 119899) (3) form the flexibility

matrix F of 119899 times 119899 dimension (4) inverse the flexibility matrixto obtain the stiffness matrix K

119905


(1) FE Model Similar to the construction process of atransmission tower the global stiffness andmassmatrices of atransmission tower-line system in the GCS can be establishedby combining the stiffness and mass matrices of towers andlines in the GCS by using the FE method

K =

119899towersum

119894=1

K(119894)119905

+

119899linesum

119895=1

K(119895)119897

M =

119899towersum

119894=1

M(119894)119905

+

119899linesum

119895=1

M(119895)119897

(13)

where 119899tower and 119899line are the numbers of towers andtransmission lines in a transmission tower-line systemrespectively

(2) MDOF Equivalent Model As discussed above the analyt-ical model of a transmission tower-line system constructedby using the 3D tower model and the cable model maybe very complicated and time-consuming in the numeri-cal computation Therefore a MDOF equivalent model of


Mn Mn

M1

M2

M3

M1

M2

M3

(a)

Mn

M1

M2

M3

m1

m1

m2

m2

m3

m3

(b)

Figure 3 Analytical model of a transmission tower-line system (a) In-plane vibration (b) Out-of-plane vibration

the transmission tower-line system can be developed bycombining the 2D tower model and the equivalent linemodel

For the transmission tower-line system the kineticenergy can be expressed in terms of the generalized coordi-nates and their first time derivatives and the potential energycan be expressed in terms of the generalized coordinatesalone In addition the virtual work which is performed bythe nonconservative forces as they act through the virtualdisplacements caused by an arbitrary set of variations in thegeneralized coordinates can be expressed as a linear functionof those variations In mathematical terms the above threestatements are expressed in the form

119879 = 119879 (1199021 1199022 119902

119873 1199021 1199022 119902

119873)

119881 = 119881 (1199021 1199022 119902

119873)

120575119882119899119888

= 11987611205751199021+ 11987621205751199022+ sdot sdot sdot + 119876

119873120575119902119873

(14)

where the coefficients 1198761 1198762 119876

119873 are the general-

ized forcing functions corresponding to the coordinates1199021 1199022 119902

119873 respectively

The analytical model of transmission tower-line systemis displayed in Figure 3 The kinetic energy 119879 and potentialenergy 119880 of the coupled system are

119879 =

119899towersum

119894=1

119879(119894)

119905+

119899linesum

119895=1

119879(119895)

119897

119880 =

119899towersum

119894=1

119880(119894)

119905+

119899linesum

119895=1

119880(119895)

119897

(15)

By substituting (15) into the Lagrange equation the motionof equation of a transmission tower-line system can be deter-mined by computing the partial differential of the kineticenergy 119879 and potential energy 119880 to generalize coordinatesand their first time derivatives

3 Wind Responses ofTransmission Tower-Line System

Transmission tower connected by many lines has morecomplex structural geometries and behaviour than commonself-supported towers Transmission tower-line system isa typical wind sensitive structure and wind loading oftencontrols the structural design of transmission tower-linesystem [20 21]The response of structures towind actionmayinvolve a wide range of structural actions including resultantforces bending moments cable tensions and deflectionsand acceleration The transmission lines being relativelyslack under dead load together with the behaviour of thetower and the conductors make the system very nonlinearIt was considered that since time history analysis takes intoaccount nonlinearity this analysis is more accurate than themultimodal spectral analysis

31 Performance Subjected to Common Wind Loading Earlystudies on guyed towers for transmission lines were focusedon the galloping phenomenon [23 24] Later works on thedynamic wind loading for transmission tower-line systemfor example the studies of Yasui et al [25] and Battistaet al [26] did not involve flexible-type structures such asguyed towers Liew and Norville [27] presented a methodfor studying the response of a transmission tower struc-tural system subjected to wind loads The wind speedsand the loads from the conductors were considered asthe loadings on the transmission tower structural systemThe data were used to determine the frequency responsefunctions of the transmission tower structural system whichprovided a measure of response Yasui et al [25] describeda method for analyzing wind-induced vibrations of powertransmission towers coupled with power lines They alsodiscussed the influence on the response characteristics ofdifferences in transmission support systems and the differ-ences between peak factors computed from a time seriesand from the power spectrum density Battista et al [26]proposed a new analytical-numerical modelling for thestructural analysis of transmission line towers under windaction for stability assessment in a design stage A simplified


(a) (b) (c) (d) (e)

Figure 4 Load patterns for performance analysis of transmission tower (a) rectangular (b) inverted triangular (c) first mode (d) powerlaw and (e) tornado

two-degree-of-freedom analytical model is also presentedand shown to be a useful tool for evaluating the systemfundamental frequency in early design stages Loredo-Souzaand Davenport [28] examined the influence of the designmethodology in the response of transmission towers to windloading The Davenport gust response factor was comparedwith the statistical method using influence lines From theresults it can be concluded that the incorporation of thedynamic properties of transmission structures in the designmethodologies is needed and that the statisticalmethod usinginfluence lines is a more correct approach since it allowsfor the inclusion of a larger number of factors in the designmethodology

The transmission tower-line systems become importantinfrastructures in modern societies and their wind-inducedresponses are an essential and practical task in the safetyassessmentOkamura et al [29] carried out thewind responseanalysis of a transmission tower in a mountainous area basedon full-scale measurements The wind response analysisresults for the blowdown flow on the leeward slope of themountain corresponded closely with the measurements Theanalytical results demonstrate that the evaluation of the blow-down angle is also important in the wind response analysis ofthe transmission tower in the mountainous area Liu and Li[30] presented an analytical framework to evaluate the along-wind-induced dynamic responses of a transmission towerTwo analytical models and a new method were developedOne was a higher mode generalized force spectrummodel ofthe transmission tower and the other was an analytical modelthat includes the contributions of the higher modes derivedas a rational algebraic formula to estimate the structuraldisplacement response A new approach was developed byapplying load with displacement (ALD) instead of forceto solve the internal force of transmission tower It wasfound that the ALDmethod can avoid calculating equivalentstatic wind loads compared with conventional methods Theimportance of the dynamic response of guyed towers fortransmission lines under wind loading was evaluated byGani and Legeron [31] The research objective was to verifyif the simplified static-equivalent approach provided in thecurrent transmission line codes is sufficient for this typeof flexible tower It was found that the static-equivalentapproach may underestimate the possible dynamic response

Similar investigations on wind-induced dynamic responseswere carried out by Hou et al [32] and Li et al [33]

The numerical simulation of transmission tower-linesystemsrsquo progressive collapse performance is considered asa major research hotspot and significant project due tothe increasing number of wind-induced collapse accidentsrecently To assess the collapse risk of transmission line struc-tures subject to natural hazards it is important to identifywhat hazard may cause the structural collapse Zhang andLi [34] introduced a new method termed as the probabilitydensity evolution method (PDEM) so as to accurately com-pute the dynamic response and reliability of a transmissiontower The random parameters of the wind stochastic fieldsuch as the roughness length themeanwind velocity and theprobability density functions were investigated It was foundthat not only the statistic quantities of the dynamic responsebut also the instantaneous probability density function of theresponse and the time-varying reliability can be determinedbased on the proposedmethodThe results demonstrated thatthe PDEM is feasible and efficient in the dynamic responseand reliability analysis of wind-excited transmission towers

Banik et al [35] assessed capacity curves for transmissionline towers under wind loading The assessment was per-formed by using a nonlinear static pushover (NSP) analysisand incremental dynamic analysis (IDA) using different loadpatterns as shown in Figure 4 For the IDA temporally andspatially varying wind speeds were simulated based on powerspectral density and coherence functions Numerical resultsindicated that the structural capacity curves of the towerdetermined from theNSP analysis depend on the load patternand that the curves determined from the nonlinear staticpushover analysis were similar to those obtained from IDAFurthermore Mara and Hong [36] investigated the inelasticresponse of a self-supported transmission tower under differ-ent wind events including traditional atmospheric boundarylayer wind and downburst wind and for wind loading atdifferent directions relative to the tower The NSP analysiswas used to obtain the capacity curve of the tower defined bythe force-deformation relationship at each considered winddirection The results indicated that the yield and maximumcapacities vary with wind direction

Fei et al [37] presented a method to evaluate thestructural status of transmission lines based on dynamic


and stability analysis A long-span transmission tower-linesystem in China with a span of 1083m was taken as thereal example Nonlinear buckling analysis for both the towerand tower-line systems was performed to determine thecritical wind loads Numerical results indicated that modalfrequencies of low order modes decrease when the windvelocity increases before the structural instability happens inboth cases Therefore for the structural health monitoringof transmission lines frequency decrease of low order modeis a useful indicator to predict the happening of struc-tural instability Zhang et al [38] examined wind-inducedcollapsed performance of a transmission tower-line systemthrough numerical simulationThe finite element models forthe single tower and transmission tower-line system wereestablished to simulate wind-induced progressive collapse byusing birth-to-death element technique with the aid of thecommercial package ABAQUS It is demonstrated that thecollapse mechanism of the transmission tower-line systemdepended on the number position and last deformation ofdamage elements

Galloping of overhead transmission lines has been underinvestigation for a long time in the industrial aerodynamicsfield and is still awaiting solution It is important to under-stand the effects ofwind turbulence on galloping and to estab-lish an evaluation method for galloping of transmission linein gusty wind Ohkuma and Marukawa [39] investigated thegalloping of overhead transmission lines in gusty wind Theydiscussed the differences between galloping in smooth windand galloping in gusty wind through a numerical simulationfocusing on their behavior rather than their mechanisms Inaddition Verma and Hagedorn [40] developed a modifiedapproach of the energy balance principle by taking intoaccount in-span damping (Figure 5) The complex transcen-dental eigenvalue problem was solved for the conductor within-span fittings With the determined complex eigenvaluesand eigenfunctions a modified energy balance principle wasthen used for scaling the amplitudes of vibrations at eachresonance frequency Bending strains are then estimated atthe critical points of the conductor

32 Performance Subjected to Tornado A thunderstorm alsoknown as an electrical storm a lightning storm thunder-shower or simply a storm is a form of turbulent weathercharacterized by the presence of lightning and its acousticeffect on the Earthrsquos atmosphere known as thunder Thun-derstorms are usually accompanied by strong winds heavyrain and sometimes snow sleet hail or no precipitationat all There are several different types of thunderstormsdepending on the origin and the associated meteorologi-cal activities All types of thunderstorms can occasionallybecome severe The most severe thunderstorm is a tor-nado and another type of severe thunderstorm is the so-called downburst In many countries a large proportion offailures of transmission tower-line systems are caused bysevere thunderstorms Because the wind loads generatedby thunderstorms are not only random but time-variant aswell a time-dependent structural reliability approach forthe risk assessment of transmission tower-line system isessential However a lack of appropriate stochastic models

x

N

120596

T 120588A EI

Figure 5 Schematic view of a typical long-span transmission line

for thunderstorm winds usually makes this kind of analysisimpossible To this end Li [41] proposed a stochastic modelto realistically and accurately simulate wind loading dueto severe thunderstorms With the proposed thunderstormmodel the collapse risk of transmission line structures undersevere thunderstorms is assessed numerically based on thecomputed failure probability of the structure

Tornadoes contain the most powerful effects of all winds[4] A tornado consists of a vortex of air that develops withina severe thunderstorm and moves with respect to the groundwith speeds of the order of 20ndash100 kmhr in a path A tornadois a violently rotating column of air that is in contact withboth the surface of the earth and the cumulonimbus cloudwhich is often referred to as twister or cyclone Tornadoesare observed as funnel-shaped clouds and the tangentialspeeds are probably highest at the funnel edge and drop-offtoward the center and with increasing distance outside thefunnel Since the centrifugal forces in the tornado vertex farexceed the Coriolis forces the latter may be neglected and thegradient wind equation can be expressed as

1198812

119903

=

1

120588

sdot

119889119901

119889119903

(16)

where 119881 is the cyclostrophic wind velocity 119903 is the radialdistance from the center of the vortex 120588 is the air density andthe 119889119901119889119903 is the pressure gradient along the radius A tornadois different to downburst and microburst In a tornadohigh velocity winds circle a central point moving inwardand upward whereas in a downburst the wind is directeddownward and then outward from the surface landing pointMany transmission line and tower failures worldwide areattributed to high intensity winds associated with tornadoes

Savory et al [7] described models for the wind velocitytime histories of transient tornado and microburst eventsand the resulting loads on a lattice transmission towerA dynamic structural analysis was developed to predict atornado-induced shear failure The results from the predic-tions were encouraging in that the tornado failure appearedto concur well with evidence from the field whilst the effectof the microburst was clearly less severe Hamada et al [42]developed a numerical scheme to assess the performanceof transmission lines under tornado wind load events Thewind forces associated with these tornado fields were eval-uated and later incorporated into a nonlinear finite elementthree-dimensional model for the transmission line systemA comparison was carried out between the forces in themembers resulting from the tornadoes and those obtainedusing the conventional design wind loadsThe study revealedthe importance of considering tornadoes when designingtransmission line structures


Ground

(a) Ring vortex model

Ground

(b) Wall jet model

Figure 6 Typical models of downburst

Table 1 Types of thunderstorm winds in Australia

Type Horizontal scale DurationMicroburst 1ndash4 kilometers 2ndash4 minutesMacroburst 4ndash10 kilometers 4ndash30 minutesOutflows(gust fronts squall lines) 10ndash100 kilometers 1ndash10 hours

Ahmed et al [43] carried out the collapse and pull-downanalysis of high voltage electricity transmission towers sub-jected to cyclonic windThey presented a novel methodologydeveloped for the critical infrastructure protectionmodellingand analysis (CIPMA) capability for assessing local windspeeds and the likelihood of tower failure for a range oftransmission tower and conductor types Similar work wasconducted by Pecin et al [44] to evaluate the mechanicalglobal actions due to an approximate mathematical model ofa tornado Usage of tornadic response spectrumpractices wasproposed and particular aspects of tornadic loads on towerstructures were analyzed

33 Performance Subjected to Downburst A downburst is astrong ground-level wind system that emanates from a singlesource blowing in a straight line in all directions from thatsource Downbursts are created by an area of significant rain-cooled air that after reaching ground level spreads out inall directions producing strong winds Downbursts includemicrobursts and macrobursts [45] Microbursts are smallerand more concentrated than downbursts the physical size ofwhich is about 4 kmor less in horizontal extent Amacroburstis a large downburst The physical size of thunderstormactivities in Australia is shown in Table 1 [46] Downburstscan induce an outburst of damaging winds near the groundwith near surface speeds in excess of 50ms During thepast decade many electrical transmission tower structureshave failed during downburst The nature of the loadingimposed on a transmission tower by a downburst will dependupon the stage of the development of the event when itinteracts with the tower [7] If the downburst is close to theground and approaching touchdown then there may wellbe a significant vertical loading component on the towerHowever if the microburst has already reached the ground

and is spreading outward as it impinges upon the towerthen the main loading components will be in the horizontalplaneThere are essentially two forms of simplifiedmodels forthe wind field associated with a downburst [47 48] namelythe ring vortex model and the impinging wall jet model asillustrated schematically in Figure 6 Many studies have beenperformed to understand the behavior of transmission tower-line system under such localized wind events

Shehata et al [49] assessed the effects of varying thedownburst parameters on the performance of a transmissionline structure by taking several real towers as examples whichwere failed in Manitoba Canada during a downburst eventin 1996The spatial and time variation of the downburst windfield was examined Then the variations of the tower mem-bersrsquo internal forces with the downburst parameters werediscussed In addition the structural behavior under criticaldownburst configurations was compared to that resultingfrom the boundary layer normal wind load conditionsFurthermore they [50 51] performed the failure analysis ofa transmission tower that collapsed in Winnipeg Canadasubjected to a microburst event Their study was conductedusing a fluid-structure numerical model that was developedin-house The model was employed first to determine themicroburst parameters that are likely to initiate failure of anumber of critical members of the tower Progressive failureanalysis of the tower was then conducted by applying theloads associated with those critical configurations

Darwish et al [52] assessed the dynamic characteristicsand behavior of transmission line conductors under theturbulent downburst loading A nonlinear numerical modelwas developed and used to predict the natural frequenciesand mode shapes of conductors at various loading stagesDynamic analysis was carried out using various down-burst configurations The made observations indicated thatthe responses are affected by the background componentwhile their sonant component turns to be negligible duelarge aerodynamic damping of the conductors Darwishand Damatty [53] also investigated the behavior of self-supported transmission line towers under downburst load-ing A parametric study was performed to determine thecritical downburst configurations causing maximum axialforces for various members of a tower The sensitivity ofthe internal forces developing in the tower members to


changes in the downburst size and location was studied Thestructural behavior associated with the critical downburstconfigurations was described and compared to the behaviorunder ldquonormalrdquo wind loads

34 Performance Subjected to Typhoon The winds producedby severe tropical cyclones also known as ldquohurricanesrdquo andldquotyphoonsrdquo are the most severe wind loading on earthHowever their infrequent occurrence at particular locationsoften makes the historical record of recorded wind speeds anunreliable predictor for design wind speeds Bulk transmis-sion tower-line system is prone to strong typhoon loadingsparticularly at the open coastal terrain in cyclonic regionsThe investigation on the performance of the transmissiontower-line system subjected to typhoon is limited due to thedifficulties in collecting typhoon wind loading

Tomokiyo et al [54] reported the typhoon damageanalysis of transmission towers in mountainous regions ofKyushu Japan They have operated a network for windmeasurement NeWMeK which measures wind speed anddirection covering these mountainous areas segmenting theKyushu area into high density arrays since 1995 In particularthey discussed the wind characteristics of Typhoon Bart in1999 and the damage to towers located in the mountainousregions along with the distribution and direction of fallentrees It was observed that transmission towers were damagedby winds that became stronger due to the effect of the localterrain or by being involved in changes in tensile forces of thetransmission lines of the towers that had already collapsedThese towers were collapsed due to a combination of theabove factorsTheworld tallest transmission tower the 370mZhoushan transmission towers over the typhoon-prone seastrait was taken as an example by Huang et al [55] toexamine structural wind effects Time domain computationalsimulation approach was also employed to predict dynamicresponses of the transmission tower and the displacementbased gust response factors (GRFs) The fair comparison ofgust loading factors or GRFs was made between the results ofthe experimental approach and the computational simulationapproach which was an effective alternative way for quicklyassessing dynamicwind load effects onhigh-rise and complextower structures

35 Experiment and Field Testing for Wind Effects

(1) Wind Tunnel Test Compared to the theoretical andnumerical investigation the studies on the performance oftransmission tower-line system through experiments andfield measurement are quite limited Vortex-induced vibra-tion is a critical problem for the steel cylinders used intubular towers such as transmission towers Therefore Denget al [56] performed vortex-induced vibration tests on lull-scale cylinders to study the vibration performance of steeltubes connected with typical joints in transmission towersincluding [-shaped gusset plate connection U-shaped gussetplate connection cross-gusset connection and the flange(see Figure 7)The testing observations indicated that vortex-induced vibration can occur not only in laminar flowsbut also in turbulent flows and the amplitude decreases as

Figure 7 View of wind tunnel testing of the vortex-inducedvibration

Figure 8 Scheme of the field testing

the turbulence intensity rises In addition Deng et al [57]carried out the wind tunnel study on wind-induced vibra-tion responses of an ultra-high-voltage (UHV) transmissiontower-line system A discrete stiffness method was appliedto design the aeroelastic model on the basis of similaritytheory as shown in Figure 8 The dynamic characteristics ofthe single tower and the tower-line system were identifiedand the displacement responses at different positions wereobtained under a variety of wind speeds It was found thatthe wind-induced vibration coefficient specified by the codeis much smaller than that by testing Thus the code valueseems to be unsafe for the UHV transmission tower

Strong winds are observed commonly associated withheavy rains The wind-rain-induced vibration and damageof civil engineering structures are frequently reported inparticular for cables and transmission lines Li et al [58]carried out the testing on wind-rain-induced vibration oftransmission towers The aeroelastic models of the antelopehorn tower and pole tower were manufactured based onthe similarity theory for the wind tunnel tests The responseanalyses and experiments for the two kinds of models wereconducted under the wind-induced and wind-rain-inducedactions with the uniform and turbulent flow It was shownthat the results of wind-rain-induced responses were biggerthan those of only wind-induced responses


Figure 9 The monitored L6 transmission line tower

(2) Field Testing Savory et al [59] discussed some of thefindings arising from long-term monitoring of the windeffects on a transmission tower located on an exposed site inSouth West England Site wind speeds and foundation loadswere measured Comparisons between the measured strainsand those determined based on UK code indicated that thecode overestimatesmost of themeasured foundation loads bya moderate amount of about 14 at higher wind speeds Thistends to confirm the validity of the code for assessing designfoundation loads Furthermore Savory et al [60] presenteda comparison between the wind-induced foundation loadsmeasured on a type L6 transmission line tower (see Figure 9)during a field study in the UK and those computed usingthe UK Code of Practice for lattice tower and transmissionline design The analysis demonstrated excellent agreementbetween the code calculations and the measured results

The galloping is commonly observed in the overheadtransmission line vibration during the ice storm A methodof single channel signal processing was implemented byGurung et al [61] to discuss galloping of transmission linesbased on field data Then the same method was extendedby them [62] to identify and characterize several numbersof vibrations observed in the Tsuruga Test Line of KansaiElectric Power Company during ice storms The piecewiseapplication of Pronyrsquos method was introduced to discusstime-dependent characteristics of harmonic components inthe responses The existence of motion-induced force wasthen confirmed for galloping events by introducing theusual buffeting theory Based on full-scalemeasurement dataTakeuchi et al [63] reported on several aerodynamic damp-ing properties of two transmission towers under conditions ofstrong winds They introduced a new method of estimatingdamping properties which was applicable to the responserecord of a multidegree of freedom system such as thecoupled structure of a transmission tower and conductorsThe component of every vibration mode of the towers wasextracted from a measured time history and the accuratedamping ratios were estimated individually (see Figure 10)

4 Seismic Responses of TransmissionTower-Line System

The conventional seismic assessment of transmission towersis usually carried out by considering each tower as anindividual structure without taking the inertia coupling andthe strong traction of transmission lines into considerationIn addition many of structural engineers were used to simplyignore the wire mass or to simplify the transmission lines asa series of lumped masses affiliated to the tower in seismiccomputation Up to now the researches related to the seismicperformance of transmission tower-line systems are limitedTo this end Li et al [64] developed an analytical model forthe seismic analysis of the transmission tower-line system byconsidering the tower-line interaction To verify the validityof the proposed model the shaking-table experiments of thecoupled tower-line system were carried out as displayed inFigure 11 The results indicated that the errors of theoreticaland testing results of systemic seismic responses are withinthe acceptable range Based on the made observations asimplified analysis method was proposed tomake the seismicresponse calculation of coupled system faster and moreeffective

Taniwaki andOhkubo [65] developed an efficient optimalsynthesismethod to determine the optimum solutions for thestructural shape cross-sectional dimensions and materialtype of all member elements of large-scale transmissiontowers subjected to static and seismic loads The exampleof a cost-minimization problem for a real transmissiontower that considers not only the material costs but alsothe cost of land as objective functions was presented todemonstrate the rigorousness efficiency and reliability ofthe proposed method Lei and Chien [66] investigated thedynamic behavior of transmission towers linked togetherthrough electrical lines when subjected to a strong groundmotionThe transmission lines and the towers were modeledby using the cable elements and the 3D beam elementsrespectively both considering geometric nonlinearities Thestrength capacities and the fracture occurrences for the mainmembers of the tower were examined with the employmentof the appropriate strength interaction equations The madeobservation indicated that the ignorance of cable contribu-tion to total seismic responses especially the portion causedby the cable mass would induce significant errors in predict-ing the ultimate strength of tower members More recentlyWang et al [67] carried out the progressive collapse analysisof the transmission tower-line system under earthquake withthe aid of the commercial package ABAQUS The collapsepaths and failure positions of the power transmission towerwere obtained under different seismic excitations

Tian et al [68] studied the seismic responses of thetransmission tower-line system subjected to spatially vary-ing ground motions The towers were modeled by usingbeam elements and the transmission lines were modeled byusing cable elements considering the nonlinear geometryBoth the incoherency of seismic waves and wave traveleffects are taken into account The effects of boundaryconditions ground motion spatial variations incident angleof the seismic wave coherency loss and wave travel on


(a) Tower A (b) Tower B

Figure 10 Elevation of the example towers

(a) Photograph of the model

x

y

Line M = 05 kg

M = 3kg

M = 2kg

M = 2kg

M = 3kg

(b) Testing model

Figure 11 Elevation of testing model

the system were investigated in detail The observationsdemonstrated that the uniform ground motion at all thesupport of the system cannot provide the most critical casefor the response calculations of the transmission tower-line system In addition they [69] examined the dynamicresponses of a transmission tower-line system at a canyonsite under spatially varying ground motions The spatiallyvarying ground motions were simulated stochastically basedon an empirical coherency loss function and a filtered Tajimi-Kanai power spectral density function It was found thatneglecting motion spatial variations may lead to a substantialunderestimation of the responses of the transmission tower-line system during strong earthquakes Furthermore Li et al[70] analyzed the effects of multicomponent multisupportexcitations on the responses of a transmission tower-linesystem Multicomponent and multisupport earthquake inputwaves were generated based on the code for the seismicdesign of electrical installations An extensive parametricstudy was conducted to investigate the behavior of thetransmission tower-line system Similar investigations wereconducted byBai et al [71] to study the nonlinear responses of

a transmission tower-line systemon a heterogeneous site sub-jected to multicomponent spatially varying ground motionsThe made observations revealed that the multisupport andmulticomponent earthquake excitations with considerationof the site effects should be considered in a reliable seismicresponse analysis of the transmission tower-line system

5 Ice-Induced Response of TransmissionTower-Line System

Temperature load is a typical environmental loading actingon the civil engineering structures in particular in somecold regions [72ndash74] Ice load and its effects on transmissiontower-line system have been substantially considered in thedesign construction and maintenance Ice shedding canbe observed when the transmission line and the conductorare subjected to the increasing environmental loading anddynamic excitations (see Figure 12) Shedding of the icethat accreted on transmission line cables is a common andpractical issue in cold regions across the world The fallingof ice chunks may result in high-amplitude vibration of


Figure 12 Accreted ice of the transmission line section

the deiced transmission lines and induce intensive dynamicforces [75] Bundle collapse of a transmission line occurswhen the bundle rotation exceeds a critical angle so that thebundle loses its stability [76 77] Ice shedding may easilyinduce electrical andmechanical accidents and thereby causea serious damage to transmission tower-line system whichattracts more and more attention across the world Havardand Dyke [78] reviewed ice-related dynamic problems onoverhead lines including ice shedding and bundle rolling

Jamaleddine et al [79] investigated the ice shedding froma two-span section using the commercial FE analysis softwareADINA They carried out a total of 44 tests on a reduced-scale two-span model to study the effects of ice sheddingon overhead lines Model predictions were validated on asmall-scale laboratory model McClure et al [80 81] studiedthe effects of ice thickness partial shedding and differentline parameters on the dynamic response of ice shedding ontransmission lines by a similar numerical approach Jakse etal [82] developed a numerical model to examine the ice-shedding effects of a 110 kV overhead power line in SloveniaA single-span and three-span FE models of conductorswere established in the computation The made observationsdemonstrated that the deflected line configuration and large-amplitude oscillations resulting from load shedding wereproblematic The situation was corrected by the utility onsome line sections by installing interphase long insulatingrod spacers Kalman et al [83] established a nonlinear FEmodel for ground wires by ADINA and several ice-sheddingscenarios were studied with variables including span lengthand pulse-load characteristics Kollar and Farzaneh [84]numerically examined the conductor vibration following iceshedding from one subconductor in a bundle Furthermorethey [85] presented a differentmodeling approach to examinethe dynamic behavior of a spacer damper located at midspanin twin triple and quad bundles after ice shedding

Fengli et al [86 87] investigated dynamic responses oftransmission tower-line system under ice shedding The 3DFE model of a tower-conductor-wire-insulator system wasestablished by using commercial package ANSYS and thedynamic responses induced by the ice shedding were ana-lyzed by considering different loading scenarios as shown inFigure 13 Many factors were considered in the ice-sheddingsimulations such as tower-line coupled effect phase combina-tion of the ice-shedding conductors thickness of the accreted

ice length of the ice-shedding span and elevation differenceEffects of different factors on the dynamic responses of jump-ing heights loads at the end of insulators and the forces oftransmission tower were also studied The made observationindicated that stress ratios of members at the tower headunder design ice thickness exceed the permitted values undera large intensity of ice shedding In addition Yang et al [88]also analyzed the unbalanced force of the transmission tower-line system in heavy icing areas A seven-continuous-spanconductor-string model of transmission lines was developedto examine the effects of design parameters which includedthe loading mode of accreted ice the eccentricity of accretedice thewind velocity the ice thickness the icing rate the spanlength the elevation difference and the span difference

Xie and Sun [89] studied the failure mechanism of trans-mission towers under ice loads and investigated the pertinentretrofitting strategy for increasing the load-carrying capacityof the tower An experimental study was conducted on twopairs of subassemblages of a typical 500 kV transmissiontower of the same type as those suffered the most severedamage during the ice disaster in South China in 2008 (seeFigure 14)Themechanical behavior failuremode strain anddeformation at critical points of the specimens were studiedThemade observations revealed that buckling of themain legwas the predominant failure mode of structures It was foundthat the addition of the diaphragm significantly improved themechanical performance of transmission towers by reducingthe torsional effect on main members and inhibiting the out-of-plane deformation of diagonal braces

Kollar and Farzaneh [90] investigated the ice sheddingfrom conductor bundles through both numerical simulationand experiment A FE model was developed to predict thetransversal line motion as well as bundle rotation and tosimulate shedding of concentrated loads The experimentalsimulation was implemented by load shedding tests on asmall-scale laboratory model Numerical model predictionswere validated by comparing them to observations obtainedfrom experiments and full-scale tests Yang et al [91] carriedout the analysis of the dynamic responses of a prototypeline from iced broken conductors A full-scale transmissionline section of three continuous spans was established andsteel cables were used to simulate the iced conductors byconsidering the equivalent mass of the accreted ice Brokenconductor experiments were carried out for different types ofconductors and ice thickness Time histories of the tensionsand displacements at the middle of conductor spans weremeasuredThe experimental results indicated that the impacteffect is more significant for the location nearer to thebreak point The dynamic impact factors decrease with theincrease of the ice thickness and the impact factors ofconductors without accreted ice are much higher than thoseof conductors with accreted ice

6 Vibration Control of TransmissionTower-Line System

Conventional disaster-resistant design of transmission tower-line system is based on the ductility of the structure thatdissipates vibrating energy induced by dynamic excitations


(a) Initial accreted ice (b) Uniform ice shedding (c) Nonuniform shedding

Figure 13 Ice-shedding scenarios

Figure 14 Failure phenomena of single-panel subassemblage with-out diaphragms

while accepting a certain level of structural damage An alter-native approach to prevent catastrophic damage of transmis-sion tower-line system is to install control devices Currentstudies on the vibration mitigation of transmission tower-line systems focus on the application of dynamic absorbersand energy-dissipating dampers Different types of energy-dissipating dampers have been developed recently as analternative approach for dynamic mitigation of transmissiontower-line system The dampers can be manufactured as anaxial member to replace common structural members of atruss tower and thus it avoids the additional occupancyof structural space Furthermore passive and semiactivedampers can reduce dynamic responses of all mode shapesof the transmission tower-line system Figure 15 displays atypical installation scheme of energy-dissipating dampers ina transmission tower

The equation of motion of the tower-line system withcontrol devices subjected to dynamic excitations can beexpressed as

Mx (119905) + Cx (119905) + Kx (119905) = P (119905) +Hu (119905) (17)

whereM C andK are mass damping and stiffness matricesof the transmission tower-line system respectively x(119905) x(119905)and x(119905) are the displacement velocity and accelerationresponses with respect to the ground respectively P(119905) isthe dynamic excitations u(119905) is the force provided by control

Figure 15 Installation scheme of energy-dissipating dampers ontransmission tower

devices for suppressing dynamic vibration and H is theinfluence matrix for u(119905)

Different types of semiactive devices can be developedto equip control devices with actively controlled parametersforming a semiactive yet stable and low-power consumingdamping system Chen et al [22 92] firstly proposed a novelapproach for the semiactive control of transmission tower-line system under dynamic excitations by using magne-torheological (MR) dampers MR dampers are typical smart(semiactive) dampers and may overcome the shortcomingsof dynamic absorbers because of their excellent controlperformance A dynamic iteration process was developedfor the numerical simulation of the dynamic responses ofthe transmission tower-line system Two semiactive controlstrategies were proposed for the vibration mitigation oftower-line systemThe first one was based on fixed incrementof controllable damper force as expressed in

119865119889(119905 + Δ119905) = 119865

119889(119905) + 120572 sdot 119865

119889(119905) (

119889 (119905) = 0)

119865119889(119905 + Δ119905) = 119865

119889(119905) minus 120572 sdot 119865

119889(119905) (

119889 (119905) = 0)

(18)

where 119865119889(119905) is the controllable Coulomb damping at time

instant 119905 120572 is the increment coefficient of the dampingforce and

119889(119905) is the slipping velocity of MR damper at


0

1

2

3

4

5

6

7

8

9

Mas

s

00 02 04 06

Peak displacement (m)

Original structurePassive-offPassive-onSemi-active number 1Semi-active number 2

(a) In-plane vibration

0

1

2

3

4

5

6

7

8

9

Mas

s

00 02 04


Original structurePassive-offPassive-onSemiactive number 1Semiactive number 2

(b) Out-of-plane vibration

Figure 16 Comparison of control performance of peak displacement

time instant 119905The second one was a clipped-optimal strategybased on fuzzy control principle as expressed in

119865119889(119905) =

min [119886119887119904 [119870119889(119909119887minus 119890)] minus 119865

0 119865max]

(119906 (119905) sdot 119906119891

(119905) gt 0

10038161003816100381610038161003816119906119891

(119905)

10038161003816100381610038161003816gt |119906 (119905)|)

119865min (other cases) (19)

where 1198650is a small adjustable quantity 119865max and 119865min are

the coulomb damper forces corresponding to the 120591119910max and

120591119910min respectively and 119906

119891

(119905) is the active control forcedetermined based on fuzzy rules A real transmission tower-line system constructed in Southern China was taken asan example to examine the feasibility and reliability of theproposed control approach In addition a parametric studywas conducted in order to examine the effects of bracestiffness wind loading intensity and parameters of MRfluids on the control performance The results as shown inFigure 16 demonstrate that the MR dampers can be utilizedon thewind-induced vibration control of transmission tower-line system because of its simple configuration as well asits satisfactory energy-dissipating capacity if the damperparameters are optimally determined

Chen et al [93] proposed an integrated approach torealize both the vibration control and the damage detectionof a transmission tower-line system subjected to seismicexcitation by using semiactive friction dampers as shown inFigure 17The semiactive control force 119906(119905) depends on either

k = EAL

S e

uu

Figure 17 Mechanical model of a semiactive friction damper

the sticking or the slipping state of the damper and it can bewritten as [94 95]

119906 (119905) =

119891119896

(119905) if 10038161003816100381610038161003816119891119896

(119905)

10038161003816100381610038161003816lt

10038161003816100381610038161003816119891119889

(119905)

10038161003816100381610038161003816(sticking)

119891119889

(119905) if 10038161003816100381610038161003816119891119896

(119905)

10038161003816100381610038161003816ge

10038161003816100381610038161003816119891119889

(119905)

10038161003816100381610038161003816(slipping)

119891119896

(119905) = 119896119889

[119889 (119905) minus 119890 (119905)]

(20)

in which 119896119889 is the spring stiffness (brace stiffness) of the semi-

active friction damper 119891119889(119905) and 119891119896

(119905) are the friction forceand axial force of a semiactive friction damper respectively119889(119905) denotes the axial displacement between the two ends ofthe friction damper and 119890(119905) is the slip deformation of thefriction damper

Two semiactive control strategies were proposed for theseismic vibration mitigation The first one was a clipped-optimal strategy based on fuzzy control principle and theother one was a strategy based on the fixed increment ofcontrollable damper forces A damage detection scheme wasdeveloped in the time domain to identify stiffness damage ofthe transmission tower A real transmission tower-line systemconstructed in China was taken as an example to examine


minus06

00

06

Time (s)

Disp

lace

men

t (m

)Ve

loci

ty (m

s)

Floor no 9

minus4minus2

0

2

4

Floor no 9

minus60minus30

03060

Acce

lera

tion

(ms

2 )

Original structureSemi-active number 1

Floor no 9

0 10 20 30 40 50

Time (s)0 10 20 30 40 50

Time (s)0 10 20 30 40 50


minus03

00

03

Floor no 9

minus2minus1

0

1

2

Floor no 9

minus20

0

20


Floor no 9

Time (s)0 10 20 30 40 50

Time (s)0 10 20 30 40 50

Time (s)0 10 20 30 40 50

Disp

lace

men

t (m

)Ve

loci

ty (m

s)

Acce

lera

tion

(ms

2 )


Figure 18 Control performance on top of the transmission tower

the feasibility and reliability of the proposed vibration controlapproach and damage detection approach Figure 18 indi-cated the control performance on top of the transmissiontower The results demonstrated that the incorporation offriction dampers into the transmission tower-line system cansubstantially suppress the earthquake-induced responses ofthe transmission tower The damage size and location of thetransmission tower can be accurately identified even withnoise contamination

In reality conventional dynamic design of thetransmission-tower line system by using control devicesis quite complicated to be carried out by the commonstructural engineers To this end Chen et al [96] proposeda method for the wind-resistant design of the transmissiontower-line system by using viscoelastic dampers Theequivalent damping ratio of the wind-excited transmissiontower incorporated with viscoelastic dampers 120577

lowast

119895can be

determined by

120577lowast

119895=

2120577119904119895120593119879

119895K119878120593119895+ 120578119863119895120593119879

119895K119863120593119895

2120593119879119895(K119878+ K119863)120593119895

(21)

where 120585119904119895is the critical damping ratio of the 119895th mode shape

120593119895is the 119895th mode shape of the controlled tower and K

119878and

K119863are the stiffnessmatrices of the tower and the contribution

matrix of viscoelastic dampers to the structural stiffnessmatrix

The practical method of the wind-resistant design wasdeveloped based on the Chinese design code A real trans-mission tower-line system constructed in China was takenas the example to examine the feasibility and reliability ofthe proposed approach Figure 19 displays the displacementresponses of the transmission towerwithwithout viscoelasticdampersThe observations demonstrated that the viscoelasticdampers can be utilized in the wind-resistant design oftransmission tower-line system because of its simple configu-ration as well as satisfactory control performanceThe designmethodproposed can also be applied towind-resistant designof civil engineering structures installed with other energy-dissipating devices

Another typical control device commonly utilized in civilengineering structures is the tuned mass damper (TMD)TMD can reduce the structural dynamic responses to someextent while it requires one or more large additional massesOwing to the inherent nature of TMD it can only abate thevibration of tunedmode shapes instead of the global dynamicresponses Tian et al [97] investigated the seismic controlof power transmission tower-line coupled system subjectedto multicomponent excitations The equation of motion ofa transmission tower with TMD under multicomponentexcitations was established The structural seismic responseswith geometric nonlinearity were computed in the timedomain The optimal design of the transmission tower-linesystem with TMD was determined based on different massratio The effects of wave travel coherency loss and differentsite conditions on the system without and with control were


0

2

4

6

8

10

00 05 10Displacement (m)

Floo

r

Original structuresWith dampers


0

2

4

6

8

10


Floo

rOriginal structuresWith dampers


Figure 19 Displacement responses of the transmission tower withwithout viscoelastic dampers

Steel pipe

Mass block Viscoelastic materialFigure 20 Three-dimensional diagram of a pounding TMD

examined respectively More recently a new type of TMDthe pounding tuned mass damper (PTMD) as shown inFigure 20 was proposed by Zhang et al [98] to examine theseismic resistant performance of a transmission tower In thePTMD a limiting collar with viscoelastic material laced onthe inner rim is installed to restrict the stroke of the TMDand to dissipate energy through collision The poundingforce is modeled based on the Hertz contact law whereasthe pounding stiffness is estimated in a small-scale test A55m transmission tower was taken as the example to verifythe validity of the PTMD through numerical simulationHarmonic excitation and time-history analysis demonstratedthe PTMD superiority over the traditional TMD

7 Concluding Remarks

An overview is presented in this study on research advancesin the analysis of transmission tower-line systemswith special

emphasis laid upon the response assessment and vibrationcontrol The research activity going on around the worldin terms of wind-induced responses seismic responsesice effects and vibration control is reviewed respectivelyIt is addressed in this review that analytical approachesbased on the transmission tower-line system are promisingin comparison with traditional techniques The approachesbased on the tower-line system not only provide reasonableobservations but also have the distinguished superiority inexploring the dynamic interaction between the tower andlines when subjected to dynamic excitations The investiga-tion of the dynamic performance and control approaches ofthe transmission tower-line systems is not over yet There arestill difficulties in the researches and the main challenges andfuture development trends are as follows

(1) Development and improvement of analytical modelsof tower-line systems are still expected From the viewit can be seen that recently there have been innovativeapplications and improvement of the analytical mod-els Many models for transmission lines have beenproposed to simulate the dynamic responses of theline in a more accurate and quick manner with thenonlinearity Therefore the analytical models of thetower-line system could be improved accordingly bycombining the newly developed cable models withthe conventional tower model which is commonlyconstructed by using the FE method to form morepowerful models for analyzing structural dynamicresponses Thus further studies on analytical modelsare necessary and imperative for the assessment andcontrol of the linear and nonlinear dynamic responsesof tower-line systems


(2) Tremendous field measurement demonstrates thatthe wind loads acting on towers and lines are quitecomplicated in particular in the regions close tocoastal areasThe loadingmodels and patterns for theextreme wind events such as typhoon downburstand tornado are quite different to that of commonmonsoonwindsUp to now the studies on the loadingmodels of transmission tower-line system subjectedto extreme winds are still very limited The damagefailure and collapse of transmission towers and lineshave been frequently reported Therefore wind load-ing on transmission tower-line system is a practicalyet challenging issue that should be investigated indetail in the future

(3) Similar to that of the winds the loading modelsand effects of other dynamic excitations such asearthquake and ice shedding still deserve furtherinvestigation The investigation of seismic damagesindicates that the dynamic interaction between thetruss tower and the soil may be intensive under strongearthquakes Furthermore the span of the transmis-sion line is quite large in comparison with commoncivil engineering structuresThus themultiexcitationeffects of the transmission tower-line system shouldbe taken into consideration in detail

(4) Transmission lines with long span are prone to thegalloping under accumulated snow and ice whichis an important factor to induce the cable ruptureand tower failure The mechanism of galloping andinduced instability of the tower-line system is still notclear and the analytical models and approaches forthe evaluation on the dynamic stability of tower-linesystem should be further examined

(5) The widely reported disasters of transmission tower-line systems around the world make it clear thatthe structures cannot avoid damage and failureunder extreme loadings such as typhoon downburstand strong earthquake even though the system isdesigned based on the current specifications andcodes The major reason is that the loading patternsspecified in the codes cannot depict the extreme load-ings and the design method is performed based onstatic analysis instead of nonlinear dynamic analysison the interaction of tower-line systems Accordinglyreasonable methods for the performance assessmentof the transmission tower-line system deserve furtherinvestigation

(6) The experiment and field measurement are consid-ered as a promising and powerful approach in theperformance assessment of transmission tower-linesystems Comparative studies of testing observationswith those from the theoretical computation andnumerical simulation are limited and needed to bemore conducted and addressed It is found that thetested dynamic properties of the transmission towerare commonly different to those based on the finiteelement model This is a practical yet difficult issue

while the model updating methods of transmissiontower-line systems have not been reportedThereforeeffective model updating approaches are necessary toaccurately predict the structural responses

It is clear that there still exist some shortcomings in theperformance assessment and vibration control techniquesof the transmission tower-line system The benefits of thecurrent technology far outweigh the problems of not usingthemThis is evident by the tremendous amount of contribu-tions from the scientific community for further developingcorresponding novel technology in the real application oftransmission tower-line systems To this end great effortsshould be taken to improve the analytical models andapproaches in the near further The manifestation of theperformance assessment and vibration control technology oftransmission tower-line systems is warmly expected

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors are grateful for the financial support fromthe technological project of the Chinese Southern PowerGrid Co Ltd (Grant K-GD2013-0783) the National NaturalScience Foundation of China (Grant 51178366) the FokYing-Tong Education Foundation (Grant 131072) and theFundamental Research Funds for the Central Universities(WUT 2013-II-015)

References

[1] B Chen Y L Xu and W L Qu ldquoEvaluation of atmosphericcorrosion damage to steel space structures in coastal areasrdquoInternational Journal of Solids and Structures vol 42 no 16-17pp 4673ndash4694 2005

[2] B Chen and Y L Xu ldquoA new damage index for detectingsudden change of structural stiffnessrdquo Structural Engineeringand Mechanics vol 26 no 3 pp 315ndash341 2007

[3] H-F Bai T-H Yi H-N Li and L Ren ldquoMultisensors on-sitemonitoring and characteristic analysis of UHV transmissiontowerrdquo International Journal of Distributed Sensor Networks vol2012 Article ID 545148 10 pages 2012

[4] E Simiu and R ScanlanWind Effects on Structures JohnWileyand Sons New York NY USA 3rd edition 1996

[5] M K S Madugula Dynamic Response of Lattice Towers andGuyedMasts American Society ofCivil Engineers (ASCE)NewYork NY USA 2002

[6] IEC Design Criteria of Overhead Transmission Lines Inter-national Standard IEC-60826 International ElectrotechnicalCommission (IEC) Geneva Switzerland 2003

[7] E Savory G A R Parke M Zeinoddini N Toy and PDisney ldquoModelling of tornado and microburst-induced windloading and failure of a lattice transmission towerrdquo EngineeringStructures vol 23 no 4 pp 365ndash375 2001


[8] H Li and H Bai ldquoHigh-voltage transmission tower-line systemsubjected to disaster loadsrdquo Progress in Natural Science vol 16no 9 pp 899ndash911 2006

[9] ASCE ldquoGuidelines for electrical transmission line structuralloadingrdquo ASCE Manuals and Reports on Engineering Practice74 1991

[10] CSA Overhead Systems CSA C22 3 1-06 Canadian StandardsAssociation Toronto Ontario 2006

[11] CSA Design Criteria for Overhead Transmission Lines CSAC22 3 No 606828 Canadian Standards Association TorontoOntario 2006

[12] P-S Lee and G McClure ldquoElastoplastic large deformationanalysis of a lattice steel tower structure and comparison withfull-scale testsrdquo Journal of Constructional Steel Research vol 63no 5 pp 709ndash717 2007

[13] H M Irvine Cable Structure The MIT Press New York NYUSA 1981

[14] L Kempner Jr and S Smith ldquoCross-rope transmission tower-line dynamic analysisrdquo Journal of Structural Engineering vol110 no 6 pp 1321ndash1335 1984

[15] American Society of Civil Engineers ldquoGuideline for electri-cal transmission line structural loadingrdquo ASCE Manuals andReports on Engineering Practice 74 New York NY USA 1991

[16] S Ozono and J Maeda ldquoIn-plane dynamic interaction betweena tower and conductors at lower frequenciesrdquo EngineeringStructures vol 14 no 4 pp 210ndash216 1992

[17] MKleiber andTDHienTheStochastic Finite ElementMethodBasic Perturbation Technique and Computer ImplementationWiley New York NY USA 1992

[18] K J BatheFinite Element Procedures Prentice-Hall New JerseyNJ USA 1996

[19] R W Clough and J Penzien Dynamic of Structures McGraw-Hill New York NY USA 3rd edition 2003

[20] M Shinozuka and G Deodatis ldquoSimulation of stochastic pro-cesses by spectral representationrdquo Applied Mechanics Reviewsvol 44 no 4 pp 191ndash204 1991

[21] G Deodatis ldquoSimulation of ergodic multivariate stochasticprocessesrdquo Journal of Engineering Mechanics vol 122 no 8 pp778ndash787 1996

[22] B Chen J Zheng and W Qu ldquoControl of wind-inducedresponse of transmission tower-line system by using mag-netorheological dampersrdquo International Journal of StructuralStability and Dynamics vol 9 no 4 pp 661ndash685 2009

[23] Y T Tsui ldquoDynamic behavior of a pylone a chaınette line partI theoretical studiesrdquo Electric Power Systems Research vol 1 no4 pp 305ndash314 1978

[24] R K Mathur A H Shah P G S Trainor and N PopplewellldquoDynamics of a guyed transmission tower systemrdquo IEEE Trans-actions on Power Delivery vol 2 no 3 pp 908ndash916 1987

[25] H Yasui H Marukawa Y Momomura and T OhkumaldquoAnalytical study on wind-induced vibration of power trans-mission towersrdquo Journal of Wind Engineering and IndustrialAerodynamics vol 83 pp 431ndash441 1999

[26] R C Battista R S Rodrigues andM S Pfeil ldquoDynamic behav-ior and stability of transmission line towers under wind forcesrdquoJournal of Wind Engineering and Industrial Aerodynamics vol91 no 8 pp 1051ndash1067 2003

[27] S H Liew and H S Norville ldquoFrequency response function ofa transmission tower subjected to multiple loadingsrdquo Journal ofWind Engineering and Industrial Aerodynamics vol 36 no 1ndash3pp 439ndash447 1990

[28] A M Loredo-Souza and A G Davenport ldquoThe influence ofthe design methodology in the response of transmission towersto wind loadingrdquo Journal of Wind Engineering and IndustrialAerodynamics vol 91 no 8 pp 995ndash1005 2003

[29] T Okamura T Ohkuma E Hongo and H Okada ldquoWindresponse analysis of a transmission tower in a mountainousareardquo Journal ofWind Engineering and Industrial Aerodynamicsvol 91 no 1-2 pp 53ndash63 2003

[30] G Liu and H Li ldquoA new framework for evaluating along-windresponses of a transmission towerrdquo Earthquake Engineering andEngineering Vibration vol 8 no 1 pp 87ndash93 2009

[31] FGani andF Legeron ldquoDynamic response of transmission linesguyed towers under wind loadingrdquo Canadian Journal of CivilEngineering vol 37 no 3 pp 450ndash464 2010

[32] J Hou Z Sun and Y Li ldquoSimulation of turbulent windvelocity for transmission tower based on auto-regressive modelmethodrdquo Energy Procedia vol 17 pp 1043ndash1049 2012

[33] Q Li Y Junjian and L Wei ldquoRandom wind-induced responseanalysis of transmission tower-line systemrdquo Energy Procediavol 16 pp 1813ndash1821 2012

[34] L-L Zhang and J Li ldquoProbability density evolution analysison dynamic response and reliability estimation of wind-excitedtransmission towersrdquo Wind and Structures An InternationalJournal vol 10 no 1 pp 45ndash60 2007

[35] S S Banik H P Hong andG A Kopp ldquoAssessment of capacitycurves for transmission line towers under wind loadingrdquoWindand Structures An International Journal vol 13 no 1 pp 1ndash202010

[36] T G Mara and H P Hong ldquoEffect of wind direction onthe response and capacity surface of a transmission towerrdquoEngineering Structures vol 57 pp 493ndash501 2013

[37] Q Fei H Zhou X Han and J Wang ldquoStructural health mon-itoring oriented stability and dynamic analysis of a long-spantransmission tower-line systemrdquo Engineering Failure Analysisvol 20 pp 80ndash87 2012

[38] Z Zhang H Li G Li W Wang and L Tian ldquoThe numer-ical analysis of transmission tower-line system wind-inducedcollapsed performancerdquoMathematical Problems in Engineeringvol 2013 Article ID 413275 11 pages 2013

[39] T Ohkuma and H Marukawa ldquoGalloping of overhead trans-mission lines in gusty windrdquo Wind and Structures An Interna-tional Journal vol 3 no 4 pp 243ndash253 2000

[40] H Verma and P Hagedorn ldquoWind induced vibrations oflong electrical overhead transmission line spans a modifiedapproachrdquo Wind and Structures An International Journal vol8 no 2 pp 89ndash106 2005

[41] C Q Li ldquoRisk assessment of transmission line structures undersevere thunderstormsrdquo Structural Engineering and Mechanicsvol 6 no 7 pp 773ndash784 1998

[42] A Hamada A A E Damatty H Hangan and A Y ShehataldquoFinite elementmodelling of transmission line structures undertornado wind loadingrdquo Wind and Structures An InternationalJournal vol 13 no 5 pp 451ndash469 2010

[43] A Ahmed C Arthur and M Edwards ldquoCollapse and pullmdashdown analysis of high voltage electricity transmission towerssubjected to cyclonic windrdquo in Proceedings of the 9th WorldCongress on Computational Mechanics and 4th Asian PacificCongress on Computation Mechanics Bristol UK 2010

[44] T G Pecin A A D Almeida and J L Roehl ldquoTornadicmechanical global actions on transmission towersrdquo Journal ofthe Brazilian Society ofMechanical Sciences and Engineering vol33 no 2 pp 131ndash138 2011


[45] T T Fujita The Downburst Report of Projects NIMROD andJAWS University of Chicago 1985

[46] J D Holmes ldquoA review of the design of transmission linestructures for wind loadsrdquo CSIRO Research Report 93-75(M)Canberra Australia 1993

[47] M Ivan ldquoRing-vortex downburst model for flight simulationsrdquoJournal of Aircraft vol 23 no 3 pp 232ndash236 1986

[48] D D Vicroy ldquoAssessment of microburst models for downdraftestimationrdquo Journal of Aircraft vol 29 no 6 pp 1043ndash10481992

[49] A Y Shehata A A El Damatty and E Savory ldquoFinite elementmodeling of transmission line under downburst wind loadingrdquoFinite Elements in Analysis and Design vol 42 no 1 pp 71ndash892005

[50] A Y Shehata and A A El Damatty ldquoBehaviour of guyedtransmission line structures under downburst wind loadingrdquoWind and Structures An International Journal vol 10 no 3 pp249ndash268 2007

[51] A Y Shehata and A A El Damatty ldquoFailure analysis of atransmission tower during a microburstrdquoWind and StructuresAn International Journal vol 11 no 3 pp 193ndash208 2008

[52] M M Darwish A A E I Damatty and H Hangan ldquoDynamiccharacteristics of transmission line conductors and behaviourunder turbulent downburst loadingrdquo Wind and Structures AnInternational Journal vol 13 no 4 pp 327ndash346 2010

[53] M M Darwish and A A El Damatty ldquoBehavior of selfsupported transmission line towers under stationary downburstloadingrdquoWind and Structures An International Journal vol 14no 5 pp 481ndash498 2011

[54] E Tomokiyo J Maeda N Ishida and Y Imamura ldquoTyphoondamage analysis of transmission towers inmountainous regionsof Kyushu Japanrdquo Wind and Structures An International Jour-nal vol 7 no 5 pp 345ndash357 2004

[55] M F Huang W Lou L Yang B Sun G Shen and K TTse ldquoExperimental and computational simulation for windeffects on the Zhoushan transmission towersrdquo Structure andInfrastructure Engineering vol 8 no 8 pp 781ndash799 2012

[56] H Z Deng Q Jiang F Li and Y Wu ldquoVortex-inducedvibration tests of circular cylinders connected with typicaljoints in transmission towersrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 99 no 10 pp 1069ndash1078 2011

[57] H Deng R Si X Hu and C Duan ldquoWind tunnel studyon wind-induced vibration responses of a UHV transmissiontower-line systemrdquo Advances in Structural Engineering vol 16no 7 pp 1175ndash1185 2013

[58] H N Li S Y Tang and T H Yi ldquoWind-rain-induced vibrationtest and analytical method of high-voltage transmission towerrdquoStructural Engineering and Mechanics vol 48 no 4 pp 435ndash453 2013

[59] E Savory G A R Parke P Disney N Toy and M Zein-oddini ldquoField measurements of wind-induced transmissiontower foundation loadsrdquoWind and Structures An InternationalJournal vol 1 no 2 pp 183ndash199 1998

[60] E Savory G A R Parke P Disney and N Toy ldquoWind-induced transmission tower foundation loads a field study-design code comparisonrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 96 no 6-7 pp 1103ndash1110 2008

[61] C B Gurung H Yamaguchi and T Yukino ldquoIdentificationof large amplitude wind-induced vibration of ice-accretedtransmission lines based on field observed datardquo EngineeringStructures vol 24 no 2 pp 179ndash188 2002

[62] H Yamaguchi C B Gurung and T Yukino ldquoCharacterizationof wind-induced vibrations in transmission lines by single-channel field data analysisrdquo Wind and Structures An Interna-tional Journal vol 8 no 2 pp 121ndash134 2005

[63] M Takeuchi J Maeda and N Ishida ldquoAerodynamic dampingproperties of two transmission towers estimated by combiningseveral identification methodsrdquo Journal of Wind Engineeringand Industrial Aerodynamics vol 98 no 12 pp 872ndash880 2010

[64] H-N Li W-L Shi G-X Wang and L-G Jia ldquoSimplifiedmodels and experimental verification for coupled transmissiontower-line system to seismic excitationsrdquo Journal of Sound andVibration vol 286 no 3 pp 569ndash585 2005

[65] K Taniwaki and S Ohkubo ldquoOptimal synthesis method fortransmission tower truss structures subjected to static andseismic loadsrdquo Structural and Multidisciplinary Optimizationvol 26 no 6 pp 441ndash454 2004

[66] Y H Lei and Y L Chien ldquoSeismic analysis of transmission tow-ers under various line configurationsrdquo Structural Engineeringand Mechanics vol 31 no 3 pp 241ndash264 2009

[67] WMWangHN Li andL Tian ldquoProgressive collapse analysisof transmission tower-line system under earthquakerdquoAdvancedSteel Construction vol 9 no 2 pp 161ndash172 2013

[68] L Tian H Li and G Liu ldquoSeismic response of powertransmission tower-line system subjected to spatially varyingground motionsrdquo Mathematical Problems in Engineering vol2010 Article ID 587317 20 pages 2010

[69] H-N Li F-L Bai L Tian and H Hao ldquoResponse of atransmission tower-line system at a canyon site to spatiallyvarying groundmotionsrdquo Journal of ZhejiangUniversity ScienceA vol 12 no 2 pp 103ndash120 2011

[70] T Li L Hongnan and L Guohuan ldquoSeismic response of powertransmission tower-line system under multi-component multi-support excitationsrdquo Journal of Earthquake and Tsunami vol 6no 4 Article ID 1250025 2012

[71] F-L Bai H Hao K-M Bi and H-N Li ldquoSeismic responseanalysis of transmission tower-line system on a heterogeneoussite to multi-component spatial ground motionsrdquo Advances inStructural Engineering vol 14 no 3 pp 457ndash474 2011

[72] B Chen Z W Chen Y Z Sun and S L Zhao ldquoConditionassessment on thermal effects of a suspension bridge basedon SHM oriented model and datardquo Mathematical Problems inEngineering vol 2013 Article ID 256816 18 pages 2013

[73] Y Xia B Chen X-Q Zhou andY-L Xu ldquoFieldmonitoring andnumerical analysis of Tsing Ma suspension bridge temperaturebehaviorrdquo Structural Control and HealthMonitoring vol 20 no4 pp 560ndash575 2013

[74] B Chen Y Z Sun G J Wang and L Y Duan ldquoAssessment ontime-varying thermal loading of engineering structures basedon a new solar radiation modelrdquo Mathematical Problems inEngineering vol 2014 Article ID 639867 15 pages 2014

[75] V T Morgan and D A Swift ldquoJump height of overhead-line conductors after the sudden release of ice loadsrdquo TheProceedings of the Institution of Electrical Engineers vol 111 no10 pp 1736ndash1746 1964

[76] Y Matsubayashi ldquoTheoretical considerations of the twistingphenomenon of the bundle conductor type transmission linerdquoSumitomo Electric Technical Review vol 1 pp 9ndash21 1963

[77] O Nigol G J Clarke and D G Havard ldquoTorsional stability ofbundle conductorsrdquo IEEE Transactions on Power Apparatus andSystems vol 96 no 5 pp 1666ndash1674 1977


[78] D G Havard and P V Dyke ldquoEffects of ice on the dynamicsof overhead lines Part II field data on conductor gallopingice shedding and bundle rollingrdquo in Proceeding of the 11thInternational Workshop Atmospheric Icing Structures pp 291ndash296 Montreal Canada 2005

[79] A Jamaleddine G McClure J Rousselet and R BeaucheminldquoSimulation of ice-shedding on electrical transmission linesusing adinardquoComputers and Structures vol 47 no 4-5 pp 523ndash536 1993

[80] M Roshan Fekr and G McClure ldquoNumerical modelling of thedynamic response of ice-shedding on electrical transmissionlinesrdquo Atmospheric Research vol 46 no 1-2 pp 1ndash11 1998

[81] GMcClure andM Lapointe ldquoModeling the structural dynamicresponse of overhead transmission linesrdquo Computers and Struc-tures vol 81 no 8ndash11 pp 825ndash834 2003

[82] J Jakse M T Al Harash and G McClure ldquoNumerical mod-elling of snow-shedding effects on a 110 kV overhead power linein Sloveniardquo in Proceedings of the 11th International Offshore andPolar Engineering Conference pp 690ndash694 Stavanger NorwayJune 2001

[83] T Kalman M Farzaneh and G McClure ldquoNumerical analysisof the dynamic effects of shock-load-induced ice shedding onoverhead ground wiresrdquo Computers and Structures vol 85 no7-8 pp 375ndash384 2007

[84] L E Kollar andM Farzaneh ldquoVibration of bundled conductorsfollowing ice sheddingrdquo IEEE Transactions on Power Deliveryvol 23 no 2 pp 1097ndash1104 2008

[85] L E Kollar and M Farzaneh ldquoModeling the dynamic effectsof ice shedding on spacer dampersrdquo Cold Regions Science andTechnology vol 57 no 2-3 pp 91ndash98 2009

[86] Y Fengli Y Jingbo H Junke and F Dongjie ldquoNumericalsimulation on the HV transmission tower-line system under icesheddingrdquo in Proceedings of the Transmission and DistributionConference and Exposition Asia and Pacific T and D Asia pp1ndash5 Seoul Republic of Korea October 2009

[87] Y Fengli Y Jingbo H Junke and F D Jie ldquoDynamic responsesof transmission tower-line system under ice sheddingrdquo Interna-tional Journal of Structural Stability and Dynamics vol 10 no3 pp 461ndash481 2010

[88] F Yang J Yang and Z Zhang ldquoUnbalanced tension analysis forUHV transmission towers in heavy icing areasrdquo Cold RegionsScience and Technology vol 70 pp 132ndash140 2012

[89] Q Xie and L Sun ldquoFailure mechanism and retrofitting strategyof transmission tower structures under ice loadrdquo Journal ofConstructional Steel Research vol 74 pp 26ndash36 2012

[90] L E Kollar and M Farzaneh ldquoModeling sudden ice sheddingfrom conductor bundlesrdquo IEEE Transactions on Power Deliveryvol 28 no 2 pp 604ndash611 2013

[91] F L Yang J B Yang Z F Zhang H J Zhang and H J XingldquoAnalysis on the Dynamic responses of a prototype line fromiced broken conductorsrdquo Engineering Failure Analysis vol 39pp 108ndash123 2014

[92] B Chen J Zheng andW L Qu ldquoWind-induced vibration con-trol of transmission tower using magnetorheological dampersrdquoin Proceedings of International Conference on Health Monitoringof Structure Materials and Environment vol 1-2 pp 323ndash327Nanjing China 2007

[93] B Chen J Zheng and W L Qu ldquoVibration control anddamage detection of transmission tower-line system underearthquake by using friction dampersrdquo in Proceedings of the 11thInternational Symposium on Structural Engineering pp 1418ndash1425 Guangzhou China 2010

[94] Y L Xu and B Chen ldquoIntegrated vibration control and healthmonitoring of building structures using semi-active frictiondampers part I-methodologyrdquo Engineering Structures vol 30no 7 pp 1789ndash1801 2008

[95] B Chen and Y L Xu ldquoIntegrated vibration control and healthmonitoring of building structures using semi-active frictiondampers part IImdashnumerical investigationrdquo Engineering Struc-tures vol 30 no 3 pp 573ndash587 2008

[96] B Chen J Zheng and W L Qu ldquoPractical method for wind-resistant design of transmission tower-line system by usingviscoelastic dampersrdquo in Proceedings of the 2nd InternationalConference on Structural Condition Assessment Monitoring andImprovement pp 1028ndash1034 Changsha China 2007

[97] L Tian Q Q Yu and R S Ma ldquoStudy on seismic controlof power transmission tower-line coupled system under multi-component excitationsrdquoMathematical Problems in Engineeringvol 2013 Article ID 829415 12 pages 2013

[98] P Zhang G B Song H N Li and Y X Lin ldquoSeismic controlof power transmission tower using pounding TMDrdquo Journal ofEngineering Mechanics vol 139 no 10 pp 1395ndash1406 2013

International Journal of

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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



approach does not provide deep insights into inelastic andnonlinear tower behaviour under strong dynamic excitationseven though the consideration of inelastic responses canbe important [12] Furthermore the primary environmentalload considered in the design of transmission structures isthe wind load although the ice load may govern the designof transmission tower-line systems in some cold regionsTherefore the damage and failure of transmission tower-linesystems have been frequently reported across the world eventhough the towers are designed and constructed strictly basedon the specifications and codes

After that the development and application of struc-tural assessment and mitigation approaches for transmissiontower-line systems in the fields of civil and electrical engi-neering have attracted more and more attention To over-come the shortcomings of conventional approaches manyanalytical models and approaches have been proposed anddeveloped for transmission tower-line systems in recent yearswith the aid of various techniques such as wind engineeringearthquake engineering structural health monitoring andvibration control However there are still many challengesand difficulties in the performance evaluation and vibrationcontrol techniques for the practical application of trans-mission tower-line system in various service conditionsTherefore it is still essential to investigate the feasibilityvalidity and applicability of the performance assessment andcontrol approaches of the transmission tower-line systems

This paper reviews the dynamic responses and control ofthe transmission tower-line system in the last two decadesThe challenges and future trends in the disaster monitor-ing and mitigation of the transmission tower-line systemsubjected to dynamic excitations are also put forward Thestructure of the rest of the paper is as follows Section 2reviews the analytical models of transmission lines trusstowers and the coupled tower-line system which containsthe theoretical model finite element (FE) model and theequivalent model Section 3 reviews the wind responsesof the transmission tower-line system which contains thestructural performance subjected to various wind loadingssuch as common winds tornado downburst and typhoonrespectively and the experiment and field testing on windeffects Sections 4 and 5 discuss the seismic responses andice-induced responses of the transmission tower-line systemrespectively The vibration control of the transmission tower-line system is also reviewed Finally the challenges andfuture trends in the dynamic assessment and mitigationof transmission tower-line system are summarized in theconclusions


21 Model of Transmission Line

(1) Theoretical Model To examine the properties of a coupledtransmission tower-line system many analytical models aredeveloped and presented during the past two decades [13ndash16] Irvine [13] systematically investigated the cable vibrationthrough theoretical deduction and corresponding results arecommonly taken as the benchmark to assess the effectiveness

of various numerical simulating approaches Based on theconclusions provided by Irvine [13] the natural frequenciesof a transmission line for antisymmetric in-plane vibration120596119904can be expressed as

120596119904=

2119899120587

119897

radic119867

119898

(119899 = 1 2 3 ) (1)

The natural frequencies of a transmission line for the sym-metric in-plane vibration can be determined by solving thefollowing equations

119905119892

120578

2

=

120578

2

minus

4

1205822(

120578

2

)

2

120578 =

120596119904119897

radic119867119898

1205822

=

(119898119892119897)2

1198673

119864119860 (2)

where 119867 is the tensile force of a transmission line 119898 is themass of a transmission line per meter 119864 and119860 are the Youngmodulus and sectional area of a transmission line 119897 is thehorizontal span of a transmission line In addition the naturalfrequencies of a cable for out-of-plane vibration 120596V are

120596V =119899120587

119897

radic119867

119898

(119899 = 1 2 3 ) (3)

(2) FE Model A transmission line can be modelled by usingcable elements in the FE method [17ndash19] The equilibriumequation of the 119894th cable element can be established by usingthe virtual work principle based on the nonlinear FEmethodThe strainmatrix of the 119894th cable elementB(119894) is the sumof thelinear strain matrix B(119894)

119871and the nonlinear strain matrix B(119894)NL

B(119894) = B(119894)119871

+ B(119894)NL (4)

Both the linear strain matrix B(119894)119871

and the nonlinear strainmatrix B(119894)NL relate to the shape function of a certain cableelement The stiffness matrix of the 119894th cable element K(119894) inthe global coordinate system (GCS) can be expressed as thesum of the elastic stiffness matrix K(119894)

119890 displacement stiffness

matrix K(119894)119892 and the stress stiffness matrix K(119894)

120590 Consider

K(119894) = K(119894)119890

+ K(119894)119892

+ K(119894)120590 (5)

The elastic stiffness matrix K(119894)119890

can be constructed only bythe linear strain matrix B(119894)

119871 while the displacement stiffness

matrixK(119894)119892can be constructed by both the linear strainmatrix

B(119894)119871

and nonlinear strain matrix B(119894)NL The stress stiffnessmatrix K(119894)

120590is constructed by using the shape function of

the cable element and the element stress 120590 The globalstiffness matrix of a transmission line can be determined bycombining all the element stiffness matrices in the GCS

K119897=

119899119897

sum

119894=1

K(119894) (6)

where 119899119897 denotes the number of all the cable elements in atransmission line The mass matrix of the transmission line


l l

v

u

ll l ll

12057911205792

1205793 1205794 1205795

1205796

1205797h7

h6h5

h1h2

h3

(a)

m1

m2

m3

L1

L2

L3

(b)



M119897=

119899119897

sum

119894=1

M(119894) (7)


1to 1199052equals


int

1199052

1199051


1199052

1199051

120575119882line (119905) 119889119905 = 0 (8)




120585119894= 120575120579119894= 120579119894minus 1205791198940

120575119894= 120575119897119894= 119897119894minus 1198971198940minus 119897119894119904

(9)



1198940and





119894 namely 120585 and 120575 Then


119889

119889119905

(

120597119879line120597 119902119894

) minus

120597119879line120597119902119894

+

120597119880line120597119902119894

= 119876119894 (10)






120585119894and

120597119879120597




119894and 120597119880120597120575








119890and mass

matrixM(119898)119890


119886

K(119898) = T(119898)119879119886

K(119898)119890

T(119898)119886

M(119898) = T(119898)119879119886

M(119898)119890

T(119898)119886

(11)




119905and


expressed as

K119905=

119899119890

sum

119898=1

T(119898)119879K(119898)T(119898)

M119905=

119899119890

sum

119898=1

T(119898)119879M(119898)T(119898)(12)


(a)

15000

29500

55500

43000

98000

76500

66500

88500

122000

110000

(b)













119905



K =

119899towersum

119894=1

K(119894)119905

+

119899linesum

119895=1

K(119895)119897

M =

119899towersum

119894=1

M(119894)119905

+

119899linesum

119895=1

M(119895)119897

(13)




Mn Mn

M1

M2

M3

M1

M2

M3

(a)

Mn

M1

M2

M3

m1

m1

m2

m2

m3

m3

(b)




119879 = 119879 (1199021 1199022 119902

119873 1199021 1199022 119902

119873)

119881 = 119881 (1199021 1199022 119902

119873)

120575119882119899119888

= 11987611205751199021+ 11987621205751199022+ sdot sdot sdot + 119876

119873120575119902119873

(14)




119873 respectively


119879 =

119899towersum

119894=1

119879(119894)

119905+

119899linesum

119895=1

119879(119895)

119897

119880 =

119899towersum

119894=1

119880(119894)

119905+

119899linesum

119895=1

119880(119895)

119897

(15)






(a) (b) (c) (d) (e)












x

N

120596

T 120588A EI




1198812

119903

=

1

120588

sdot

119889119901

119889119903

(16)




Ground


Ground

(b) Wall jet model































x

y

Line M = 05 kg

M = 3kg

M = 2kg

M = 2kg

M = 3kg

(b) Testing model






















Mx (119905) + Cx (119905) + Kx (119905) = P (119905) +Hu (119905) (17)





119865119889(119905 + Δ119905) = 119865

119889(119905) + 120572 sdot 119865

119889(119905) (

119889 (119905) = 0)

119865119889(119905 + Δ119905) = 119865

119889(119905) minus 120572 sdot 119865

119889(119905) (

119889 (119905) = 0)

(18)





0

1

2

3

4

5

6

7

8

9

Mas

s

00 02 04 06




0

1

2

3

4

5

6

7

8

9

Mas

s

00 02 04






119865119889(119905) =

min [119886119887119904 [119870119889(119909119887minus 119890)] minus 119865

0 119865max]

(119906 (119905) sdot 119906119891

(119905) gt 0

10038161003816100381610038161003816119906119891

(119905)

10038161003816100381610038161003816gt |119906 (119905)|)





119891



k = EAL

S e

uu



119906 (119905) =

119891119896

(119905) if 10038161003816100381610038161003816119891119896

(119905)

10038161003816100381610038161003816lt

10038161003816100381610038161003816119891119889

(119905)

10038161003816100381610038161003816(sticking)

119891119889

(119905) if 10038161003816100381610038161003816119891119896

(119905)

10038161003816100381610038161003816ge

10038161003816100381610038161003816119891119889

(119905)

10038161003816100381610038161003816(slipping)

119891119896

(119905) = 119896119889

[119889 (119905) minus 119890 (119905)]

(20)






minus06

00

06

Time (s)

Disp

lace

men

t (m

)Ve

loci

ty (m

s)

Floor no 9

minus4minus2

0

2

4

Floor no 9

minus60minus30

03060

Acce

lera

tion

(ms

2 )


Floor no 9

0 10 20 30 40 50

Time (s)0 10 20 30 40 50

Time (s)0 10 20 30 40 50


minus03

00

03

Floor no 9

minus2minus1

0

1

2

Floor no 9

minus20

0

20


Floor no 9

Time (s)0 10 20 30 40 50

Time (s)0 10 20 30 40 50

Time (s)0 10 20 30 40 50

Disp

lace

men

t (m

)Ve

loci

ty (m

s)

Acce

lera

tion

(ms

2 )





lowast

119895can be

determined by

120577lowast

119895=

2120577119904119895120593119879

119895K119878120593119895+ 120578119863119895120593119879

119895K119863120593119895

2120593119879119895(K119878+ K119863)120593119895

(21)



119878and






0

2

4

6

8

10


Floo

r



0

2

4

6

8

10


Floo




Steel pipe

















Acknowledgments


References








































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










l l

v

u

ll l ll

12057911205792

1205793 1205794 1205795

1205796

1205797h7

h6h5

h1h2

h3

(a)

m1

m2

m3

L1

L2

L3

(b)



M119897=

119899119897

sum

119894=1

M(119894) (7)


1to 1199052equals


int

1199052

1199051


1199052

1199051

120575119882line (119905) 119889119905 = 0 (8)




120585119894= 120575120579119894= 120579119894minus 1205791198940

120575119894= 120575119897119894= 119897119894minus 1198971198940minus 119897119894119904

(9)



1198940and





119894 namely 120585 and 120575 Then


119889

119889119905

(

120597119879line120597 119902119894

) minus

120597119879line120597119902119894

+

120597119880line120597119902119894

= 119876119894 (10)






120585119894and

120597119879120597




119894and 120597119880120597120575








119890and mass

matrixM(119898)119890


119886

K(119898) = T(119898)119879119886

K(119898)119890

T(119898)119886

M(119898) = T(119898)119879119886

M(119898)119890

T(119898)119886

(11)




119905and


expressed as

K119905=

119899119890

sum

119898=1

T(119898)119879K(119898)T(119898)

M119905=

119899119890

sum

119898=1

T(119898)119879M(119898)T(119898)(12)


(a)

15000

29500

55500

43000

98000

76500

66500

88500

122000

110000

(b)













119905



K =

119899towersum

119894=1

K(119894)119905

+

119899linesum

119895=1

K(119895)119897

M =

119899towersum

119894=1

M(119894)119905

+

119899linesum

119895=1

M(119895)119897

(13)




Mn Mn

M1

M2

M3

M1

M2

M3

(a)

Mn

M1

M2

M3

m1

m1

m2

m2

m3

m3

(b)




119879 = 119879 (1199021 1199022 119902

119873 1199021 1199022 119902

119873)

119881 = 119881 (1199021 1199022 119902

119873)

120575119882119899119888

= 11987611205751199021+ 11987621205751199022+ sdot sdot sdot + 119876

119873120575119902119873

(14)




119873 respectively


119879 =

119899towersum

119894=1

119879(119894)

119905+

119899linesum

119895=1

119879(119895)

119897

119880 =

119899towersum

119894=1

119880(119894)

119905+

119899linesum

119895=1

119880(119895)

119897

(15)






(a) (b) (c) (d) (e)












x

N

120596

T 120588A EI




1198812

119903

=

1

120588

sdot

119889119901

119889119903

(16)




Ground


Ground

(b) Wall jet model































x

y

Line M = 05 kg

M = 3kg

M = 2kg

M = 2kg

M = 3kg

(b) Testing model






















Mx (119905) + Cx (119905) + Kx (119905) = P (119905) +Hu (119905) (17)





119865119889(119905 + Δ119905) = 119865

119889(119905) + 120572 sdot 119865

119889(119905) (

119889 (119905) = 0)

119865119889(119905 + Δ119905) = 119865

119889(119905) minus 120572 sdot 119865

119889(119905) (

119889 (119905) = 0)

(18)





0

1

2

3

4

5

6

7

8

9

Mas

s

00 02 04 06




0

1

2

3

4

5

6

7

8

9

Mas

s

00 02 04






119865119889(119905) =

min [119886119887119904 [119870119889(119909119887minus 119890)] minus 119865

0 119865max]

(119906 (119905) sdot 119906119891

(119905) gt 0

10038161003816100381610038161003816119906119891

(119905)

10038161003816100381610038161003816gt |119906 (119905)|)





119891



k = EAL

S e

uu



119906 (119905) =

119891119896

(119905) if 10038161003816100381610038161003816119891119896

(119905)

10038161003816100381610038161003816lt

10038161003816100381610038161003816119891119889

(119905)

10038161003816100381610038161003816(sticking)

119891119889

(119905) if 10038161003816100381610038161003816119891119896

(119905)

10038161003816100381610038161003816ge

10038161003816100381610038161003816119891119889

(119905)

10038161003816100381610038161003816(slipping)

119891119896

(119905) = 119896119889

[119889 (119905) minus 119890 (119905)]

(20)






minus06

00

06

Time (s)

Disp

lace

men

t (m

)Ve

loci

ty (m

s)

Floor no 9

minus4minus2

0

2

4

Floor no 9

minus60minus30

03060

Acce

lera

tion

(ms

2 )


Floor no 9

0 10 20 30 40 50

Time (s)0 10 20 30 40 50

Time (s)0 10 20 30 40 50


minus03

00

03

Floor no 9

minus2minus1

0

1

2

Floor no 9

minus20

0

20


Floor no 9

Time (s)0 10 20 30 40 50

Time (s)0 10 20 30 40 50

Time (s)0 10 20 30 40 50

Disp

lace

men

t (m

)Ve

loci

ty (m

s)

Acce

lera

tion

(ms

2 )





lowast

119895can be

determined by

120577lowast

119895=

2120577119904119895120593119879

119895K119878120593119895+ 120578119863119895120593119879

119895K119863120593119895

2120593119879119895(K119878+ K119863)120593119895

(21)



119878and






0

2

4

6

8

10


Floo

r



0

2

4

6

8

10


Floo




Steel pipe

















Acknowledgments


References








































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a)

15000

29500

55500

43000

98000

76500

66500

88500

122000

110000

(b)













119905



K =

119899towersum

119894=1

K(119894)119905

+

119899linesum

119895=1

K(119895)119897

M =

119899towersum

119894=1

M(119894)119905

+

119899linesum

119895=1

M(119895)119897

(13)




Mn Mn

M1

M2

M3

M1

M2

M3

(a)

Mn

M1

M2

M3

m1

m1

m2

m2

m3

m3

(b)




119879 = 119879 (1199021 1199022 119902

119873 1199021 1199022 119902

119873)

119881 = 119881 (1199021 1199022 119902

119873)

120575119882119899119888

= 11987611205751199021+ 11987621205751199022+ sdot sdot sdot + 119876

119873120575119902119873

(14)




119873 respectively


119879 =

119899towersum

119894=1

119879(119894)

119905+

119899linesum

119895=1

119879(119895)

119897

119880 =

119899towersum

119894=1

119880(119894)

119905+

119899linesum

119895=1

119880(119895)

119897

(15)






(a) (b) (c) (d) (e)












x

N

120596

T 120588A EI




1198812

119903

=

1

120588

sdot

119889119901

119889119903

(16)




Ground


Ground

(b) Wall jet model































x

y

Line M = 05 kg

M = 3kg

M = 2kg

M = 2kg

M = 3kg

(b) Testing model






















Mx (119905) + Cx (119905) + Kx (119905) = P (119905) +Hu (119905) (17)





119865119889(119905 + Δ119905) = 119865

119889(119905) + 120572 sdot 119865

119889(119905) (

119889 (119905) = 0)

119865119889(119905 + Δ119905) = 119865

119889(119905) minus 120572 sdot 119865

119889(119905) (

119889 (119905) = 0)

(18)





0

1

2

3

4

5

6

7

8

9

Mas

s

00 02 04 06




0

1

2

3

4

5

6

7

8

9

Mas

s

00 02 04






119865119889(119905) =

min [119886119887119904 [119870119889(119909119887minus 119890)] minus 119865

0 119865max]

(119906 (119905) sdot 119906119891

(119905) gt 0

10038161003816100381610038161003816119906119891

(119905)

10038161003816100381610038161003816gt |119906 (119905)|)





119891



k = EAL

S e

uu



119906 (119905) =

119891119896

(119905) if 10038161003816100381610038161003816119891119896

(119905)

10038161003816100381610038161003816lt

10038161003816100381610038161003816119891119889

(119905)

10038161003816100381610038161003816(sticking)

119891119889

(119905) if 10038161003816100381610038161003816119891119896

(119905)

10038161003816100381610038161003816ge

10038161003816100381610038161003816119891119889

(119905)

10038161003816100381610038161003816(slipping)

119891119896

(119905) = 119896119889

[119889 (119905) minus 119890 (119905)]

(20)






minus06

00

06

Time (s)

Disp

lace

men

t (m

)Ve

loci

ty (m

s)

Floor no 9

minus4minus2

0

2

4

Floor no 9

minus60minus30

03060

Acce

lera

tion

(ms

2 )


Floor no 9

0 10 20 30 40 50

Time (s)0 10 20 30 40 50

Time (s)0 10 20 30 40 50


minus03

00

03

Floor no 9

minus2minus1

0

1

2

Floor no 9

minus20

0

20


Floor no 9

Time (s)0 10 20 30 40 50

Time (s)0 10 20 30 40 50

Time (s)0 10 20 30 40 50

Disp

lace

men

t (m

)Ve

loci

ty (m

s)

Acce

lera

tion

(ms

2 )





lowast

119895can be

determined by

120577lowast

119895=

2120577119904119895120593119879

119895K119878120593119895+ 120578119863119895120593119879

119895K119863120593119895

2120593119879119895(K119878+ K119863)120593119895

(21)



119878and






0

2

4

6

8

10


Floo

r



0

2

4

6

8

10


Floo




Steel pipe

















Acknowledgments


References








































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Mn Mn

M1

M2

M3

M1

M2

M3

(a)

Mn

M1

M2

M3

m1

m1

m2

m2

m3

m3

(b)




119879 = 119879 (1199021 1199022 119902

119873 1199021 1199022 119902

119873)

119881 = 119881 (1199021 1199022 119902

119873)

120575119882119899119888

= 11987611205751199021+ 11987621205751199022+ sdot sdot sdot + 119876

119873120575119902119873

(14)




119873 respectively


119879 =

119899towersum

119894=1

119879(119894)

119905+

119899linesum

119895=1

119879(119895)

119897

119880 =

119899towersum

119894=1

119880(119894)

119905+

119899linesum

119895=1

119880(119895)

119897

(15)






(a) (b) (c) (d) (e)












x

N

120596

T 120588A EI




1198812

119903

=

1

120588

sdot

119889119901

119889119903

(16)




Ground


Ground

(b) Wall jet model































x

y

Line M = 05 kg

M = 3kg

M = 2kg

M = 2kg

M = 3kg

(b) Testing model






















Mx (119905) + Cx (119905) + Kx (119905) = P (119905) +Hu (119905) (17)





119865119889(119905 + Δ119905) = 119865

119889(119905) + 120572 sdot 119865

119889(119905) (

119889 (119905) = 0)

119865119889(119905 + Δ119905) = 119865

119889(119905) minus 120572 sdot 119865

119889(119905) (

119889 (119905) = 0)

(18)





0

1

2

3

4

5

6

7

8

9

Mas

s

00 02 04 06




0

1

2

3

4

5

6

7

8

9

Mas

s

00 02 04






119865119889(119905) =

min [119886119887119904 [119870119889(119909119887minus 119890)] minus 119865

0 119865max]

(119906 (119905) sdot 119906119891

(119905) gt 0

10038161003816100381610038161003816119906119891

(119905)

10038161003816100381610038161003816gt |119906 (119905)|)





119891



k = EAL

S e

uu



119906 (119905) =

119891119896

(119905) if 10038161003816100381610038161003816119891119896

(119905)

10038161003816100381610038161003816lt

10038161003816100381610038161003816119891119889

(119905)

10038161003816100381610038161003816(sticking)

119891119889

(119905) if 10038161003816100381610038161003816119891119896

(119905)

10038161003816100381610038161003816ge

10038161003816100381610038161003816119891119889

(119905)

10038161003816100381610038161003816(slipping)

119891119896

(119905) = 119896119889

[119889 (119905) minus 119890 (119905)]

(20)






minus06

00

06

Time (s)

Disp

lace

men

t (m

)Ve

loci

ty (m

s)

Floor no 9

minus4minus2

0

2

4

Floor no 9

minus60minus30

03060

Acce

lera

tion

(ms

2 )


Floor no 9

0 10 20 30 40 50

Time (s)0 10 20 30 40 50

Time (s)0 10 20 30 40 50


minus03

00

03

Floor no 9

minus2minus1

0

1

2

Floor no 9

minus20

0

20


Floor no 9

Time (s)0 10 20 30 40 50

Time (s)0 10 20 30 40 50

Time (s)0 10 20 30 40 50

Disp

lace

men

t (m

)Ve

loci

ty (m

s)

Acce

lera

tion

(ms

2 )





lowast

119895can be

determined by

120577lowast

119895=

2120577119904119895120593119879

119895K119878120593119895+ 120578119863119895120593119879

119895K119863120593119895

2120593119879119895(K119878+ K119863)120593119895

(21)



119878and






0

2

4

6

8

10


Floo

r



0

2

4

6

8

10


Floo




Steel pipe

















Acknowledgments


References








































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a) (b) (c) (d) (e)












x

N

120596

T 120588A EI




1198812

119903

=

1

120588

sdot

119889119901

119889119903

(16)




Ground


Ground

(b) Wall jet model































x

y

Line M = 05 kg

M = 3kg

M = 2kg

M = 2kg

M = 3kg

(b) Testing model






















Mx (119905) + Cx (119905) + Kx (119905) = P (119905) +Hu (119905) (17)





119865119889(119905 + Δ119905) = 119865

119889(119905) + 120572 sdot 119865

119889(119905) (

119889 (119905) = 0)

119865119889(119905 + Δ119905) = 119865

119889(119905) minus 120572 sdot 119865

119889(119905) (

119889 (119905) = 0)

(18)





0

1

2

3

4

5

6

7

8

9

Mas

s

00 02 04 06




0

1

2

3

4

5

6

7

8

9

Mas

s

00 02 04






119865119889(119905) =

min [119886119887119904 [119870119889(119909119887minus 119890)] minus 119865

0 119865max]

(119906 (119905) sdot 119906119891

(119905) gt 0

10038161003816100381610038161003816119906119891

(119905)

10038161003816100381610038161003816gt |119906 (119905)|)





119891



k = EAL

S e

uu



119906 (119905) =

119891119896

(119905) if 10038161003816100381610038161003816119891119896

(119905)

10038161003816100381610038161003816lt

10038161003816100381610038161003816119891119889

(119905)

10038161003816100381610038161003816(sticking)

119891119889

(119905) if 10038161003816100381610038161003816119891119896

(119905)

10038161003816100381610038161003816ge

10038161003816100381610038161003816119891119889

(119905)

10038161003816100381610038161003816(slipping)

119891119896

(119905) = 119896119889

[119889 (119905) minus 119890 (119905)]

(20)






minus06

00

06

Time (s)

Disp

lace

men

t (m

)Ve

loci

ty (m

s)

Floor no 9

minus4minus2

0

2

4

Floor no 9

minus60minus30

03060

Acce

lera

tion

(ms

2 )


Floor no 9

0 10 20 30 40 50

Time (s)0 10 20 30 40 50

Time (s)0 10 20 30 40 50


minus03

00

03

Floor no 9

minus2minus1

0

1

2

Floor no 9

minus20

0

20


Floor no 9

Time (s)0 10 20 30 40 50

Time (s)0 10 20 30 40 50

Time (s)0 10 20 30 40 50

Disp

lace

men

t (m

)Ve

loci

ty (m

s)

Acce

lera

tion

(ms

2 )





lowast

119895can be

determined by

120577lowast

119895=

2120577119904119895120593119879

119895K119878120593119895+ 120578119863119895120593119879

119895K119863120593119895

2120593119879119895(K119878+ K119863)120593119895

(21)



119878and






0

2

4

6

8

10


Floo

r



0

2

4

6

8

10


Floo




Steel pipe

















Acknowledgments


References








































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













x

N

120596

T 120588A EI




1198812

119903

=

1

120588

sdot

119889119901

119889119903

(16)




Ground


Ground

(b) Wall jet model































x

y

Line M = 05 kg

M = 3kg

M = 2kg

M = 2kg

M = 3kg

(b) Testing model






















Mx (119905) + Cx (119905) + Kx (119905) = P (119905) +Hu (119905) (17)





119865119889(119905 + Δ119905) = 119865

119889(119905) + 120572 sdot 119865

119889(119905) (

119889 (119905) = 0)

119865119889(119905 + Δ119905) = 119865

119889(119905) minus 120572 sdot 119865

119889(119905) (

119889 (119905) = 0)

(18)





0

1

2

3

4

5

6

7

8

9

Mas

s

00 02 04 06




0

1

2

3

4

5

6

7

8

9

Mas

s

00 02 04






119865119889(119905) =

min [119886119887119904 [119870119889(119909119887minus 119890)] minus 119865

0 119865max]

(119906 (119905) sdot 119906119891

(119905) gt 0

10038161003816100381610038161003816119906119891

(119905)

10038161003816100381610038161003816gt |119906 (119905)|)





119891



k = EAL

S e

uu



119906 (119905) =

119891119896

(119905) if 10038161003816100381610038161003816119891119896

(119905)

10038161003816100381610038161003816lt

10038161003816100381610038161003816119891119889

(119905)

10038161003816100381610038161003816(sticking)

119891119889

(119905) if 10038161003816100381610038161003816119891119896

(119905)

10038161003816100381610038161003816ge

10038161003816100381610038161003816119891119889

(119905)

10038161003816100381610038161003816(slipping)

119891119896

(119905) = 119896119889

[119889 (119905) minus 119890 (119905)]

(20)






minus06

00

06

Time (s)

Disp

lace

men

t (m

)Ve

loci

ty (m

s)

Floor no 9

minus4minus2

0

2

4

Floor no 9

minus60minus30

03060

Acce

lera

tion

(ms

2 )


Floor no 9

0 10 20 30 40 50

Time (s)0 10 20 30 40 50

Time (s)0 10 20 30 40 50


minus03

00

03

Floor no 9

minus2minus1

0

1

2

Floor no 9

minus20

0

20


Floor no 9

Time (s)0 10 20 30 40 50

Time (s)0 10 20 30 40 50

Time (s)0 10 20 30 40 50

Disp

lace

men

t (m

)Ve

loci

ty (m

s)

Acce

lera

tion

(ms

2 )





lowast

119895can be

determined by

120577lowast

119895=

2120577119904119895120593119879

119895K119878120593119895+ 120578119863119895120593119879

119895K119863120593119895

2120593119879119895(K119878+ K119863)120593119895

(21)



119878and






0

2

4

6

8

10


Floo

r



0

2

4

6

8

10


Floo




Steel pipe

















Acknowledgments


References








































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Ground


Ground

(b) Wall jet model































x

y

Line M = 05 kg

M = 3kg

M = 2kg

M = 2kg

M = 3kg

(b) Testing model






















Mx (119905) + Cx (119905) + Kx (119905) = P (119905) +Hu (119905) (17)





119865119889(119905 + Δ119905) = 119865

119889(119905) + 120572 sdot 119865

119889(119905) (

119889 (119905) = 0)

119865119889(119905 + Δ119905) = 119865

119889(119905) minus 120572 sdot 119865

119889(119905) (

119889 (119905) = 0)

(18)





0

1

2

3

4

5

6

7

8

9

Mas

s

00 02 04 06




0

1

2

3

4

5

6

7

8

9

Mas

s

00 02 04






119865119889(119905) =

min [119886119887119904 [119870119889(119909119887minus 119890)] minus 119865

0 119865max]

(119906 (119905) sdot 119906119891

(119905) gt 0

10038161003816100381610038161003816119906119891

(119905)

10038161003816100381610038161003816gt |119906 (119905)|)





119891



k = EAL

S e

uu



119906 (119905) =

119891119896

(119905) if 10038161003816100381610038161003816119891119896

(119905)

10038161003816100381610038161003816lt

10038161003816100381610038161003816119891119889

(119905)

10038161003816100381610038161003816(sticking)

119891119889

(119905) if 10038161003816100381610038161003816119891119896

(119905)

10038161003816100381610038161003816ge

10038161003816100381610038161003816119891119889

(119905)

10038161003816100381610038161003816(slipping)

119891119896

(119905) = 119896119889

[119889 (119905) minus 119890 (119905)]

(20)






minus06

00

06

Time (s)

Disp

lace

men

t (m

)Ve

loci

ty (m

s)

Floor no 9

minus4minus2

0

2

4

Floor no 9

minus60minus30

03060

Acce

lera

tion

(ms

2 )


Floor no 9

0 10 20 30 40 50

Time (s)0 10 20 30 40 50

Time (s)0 10 20 30 40 50


minus03

00

03

Floor no 9

minus2minus1

0

1

2

Floor no 9

minus20

0

20


Floor no 9

Time (s)0 10 20 30 40 50

Time (s)0 10 20 30 40 50

Time (s)0 10 20 30 40 50

Disp

lace

men

t (m

)Ve

loci

ty (m

s)

Acce

lera

tion

(ms

2 )





lowast

119895can be

determined by

120577lowast

119895=

2120577119904119895120593119879

119895K119878120593119895+ 120578119863119895120593119879

119895K119863120593119895

2120593119879119895(K119878+ K119863)120593119895

(21)



119878and






0

2

4

6

8

10


Floo

r



0

2

4

6

8

10


Floo




Steel pipe

















Acknowledgments


References








































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation































x

y

Line M = 05 kg

M = 3kg

M = 2kg

M = 2kg

M = 3kg

(b) Testing model






















Mx (119905) + Cx (119905) + Kx (119905) = P (119905) +Hu (119905) (17)





119865119889(119905 + Δ119905) = 119865

119889(119905) + 120572 sdot 119865

119889(119905) (

119889 (119905) = 0)

119865119889(119905 + Δ119905) = 119865

119889(119905) minus 120572 sdot 119865

119889(119905) (

119889 (119905) = 0)

(18)





0

1

2

3

4

5

6

7

8

9

Mas

s

00 02 04 06




0

1

2

3

4

5

6

7

8

9

Mas

s

00 02 04






119865119889(119905) =

min [119886119887119904 [119870119889(119909119887minus 119890)] minus 119865

0 119865max]

(119906 (119905) sdot 119906119891

(119905) gt 0

10038161003816100381610038161003816119906119891

(119905)

10038161003816100381610038161003816gt |119906 (119905)|)





119891



k = EAL

S e

uu



119906 (119905) =

119891119896

(119905) if 10038161003816100381610038161003816119891119896

(119905)

10038161003816100381610038161003816lt

10038161003816100381610038161003816119891119889

(119905)

10038161003816100381610038161003816(sticking)

119891119889

(119905) if 10038161003816100381610038161003816119891119896

(119905)

10038161003816100381610038161003816ge

10038161003816100381610038161003816119891119889

(119905)

10038161003816100381610038161003816(slipping)

119891119896

(119905) = 119896119889

[119889 (119905) minus 119890 (119905)]

(20)






minus06

00

06

Time (s)

Disp

lace

men

t (m

)Ve

loci

ty (m

s)

Floor no 9

minus4minus2

0

2

4

Floor no 9

minus60minus30

03060

Acce

lera

tion

(ms

2 )


Floor no 9

0 10 20 30 40 50

Time (s)0 10 20 30 40 50

Time (s)0 10 20 30 40 50


minus03

00

03

Floor no 9

minus2minus1

0

1

2

Floor no 9

minus20

0

20


Floor no 9

Time (s)0 10 20 30 40 50

Time (s)0 10 20 30 40 50

Time (s)0 10 20 30 40 50

Disp

lace

men

t (m

)Ve

loci

ty (m

s)

Acce

lera

tion

(ms

2 )





lowast

119895can be

determined by

120577lowast

119895=

2120577119904119895120593119879

119895K119878120593119895+ 120578119863119895120593119879

119895K119863120593119895

2120593119879119895(K119878+ K119863)120593119895

(21)



119878and






0

2

4

6

8

10


Floo

r



0

2

4

6

8

10


Floo




Steel pipe

















Acknowledgments


References








































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation





















x

y

Line M = 05 kg

M = 3kg

M = 2kg

M = 2kg

M = 3kg

(b) Testing model






















Mx (119905) + Cx (119905) + Kx (119905) = P (119905) +Hu (119905) (17)





119865119889(119905 + Δ119905) = 119865

119889(119905) + 120572 sdot 119865

119889(119905) (

119889 (119905) = 0)

119865119889(119905 + Δ119905) = 119865

119889(119905) minus 120572 sdot 119865

119889(119905) (

119889 (119905) = 0)

(18)





0

1

2

3

4

5

6

7

8

9

Mas

s

00 02 04 06




0

1

2

3

4

5

6

7

8

9

Mas

s

00 02 04






119865119889(119905) =

min [119886119887119904 [119870119889(119909119887minus 119890)] minus 119865

0 119865max]

(119906 (119905) sdot 119906119891

(119905) gt 0

10038161003816100381610038161003816119906119891

(119905)

10038161003816100381610038161003816gt |119906 (119905)|)





119891



k = EAL

S e

uu



119906 (119905) =

119891119896

(119905) if 10038161003816100381610038161003816119891119896

(119905)

10038161003816100381610038161003816lt

10038161003816100381610038161003816119891119889

(119905)

10038161003816100381610038161003816(sticking)

119891119889

(119905) if 10038161003816100381610038161003816119891119896

(119905)

10038161003816100381610038161003816ge

10038161003816100381610038161003816119891119889

(119905)

10038161003816100381610038161003816(slipping)

119891119896

(119905) = 119896119889

[119889 (119905) minus 119890 (119905)]

(20)






minus06

00

06

Time (s)

Disp

lace

men

t (m

)Ve

loci

ty (m

s)

Floor no 9

minus4minus2

0

2

4

Floor no 9

minus60minus30

03060

Acce

lera

tion

(ms

2 )


Floor no 9

0 10 20 30 40 50

Time (s)0 10 20 30 40 50

Time (s)0 10 20 30 40 50


minus03

00

03

Floor no 9

minus2minus1

0

1

2

Floor no 9

minus20

0

20


Floor no 9

Time (s)0 10 20 30 40 50

Time (s)0 10 20 30 40 50

Time (s)0 10 20 30 40 50

Disp

lace

men

t (m

)Ve

loci

ty (m

s)

Acce

lera

tion

(ms

2 )





lowast

119895can be

determined by

120577lowast

119895=

2120577119904119895120593119879

119895K119878120593119895+ 120578119863119895120593119879

119895K119863120593119895

2120593119879119895(K119878+ K119863)120593119895

(21)



119878and






0

2

4

6

8

10


Floo

r



0

2

4

6

8

10


Floo




Steel pipe

















Acknowledgments


References








































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













x

y

Line M = 05 kg

M = 3kg

M = 2kg

M = 2kg

M = 3kg

(b) Testing model






















Mx (119905) + Cx (119905) + Kx (119905) = P (119905) +Hu (119905) (17)





119865119889(119905 + Δ119905) = 119865

119889(119905) + 120572 sdot 119865

119889(119905) (

119889 (119905) = 0)

119865119889(119905 + Δ119905) = 119865

119889(119905) minus 120572 sdot 119865

119889(119905) (

119889 (119905) = 0)

(18)





0

1

2

3

4

5

6

7

8

9

Mas

s

00 02 04 06




0

1

2

3

4

5

6

7

8

9

Mas

s

00 02 04






119865119889(119905) =

min [119886119887119904 [119870119889(119909119887minus 119890)] minus 119865

0 119865max]

(119906 (119905) sdot 119906119891

(119905) gt 0

10038161003816100381610038161003816119906119891

(119905)

10038161003816100381610038161003816gt |119906 (119905)|)





119891



k = EAL

S e

uu



119906 (119905) =

119891119896

(119905) if 10038161003816100381610038161003816119891119896

(119905)

10038161003816100381610038161003816lt

10038161003816100381610038161003816119891119889

(119905)

10038161003816100381610038161003816(sticking)

119891119889

(119905) if 10038161003816100381610038161003816119891119896

(119905)

10038161003816100381610038161003816ge

10038161003816100381610038161003816119891119889

(119905)

10038161003816100381610038161003816(slipping)

119891119896

(119905) = 119896119889

[119889 (119905) minus 119890 (119905)]

(20)






minus06

00

06

Time (s)

Disp

lace

men

t (m

)Ve

loci

ty (m

s)

Floor no 9

minus4minus2

0

2

4

Floor no 9

minus60minus30

03060

Acce

lera

tion

(ms

2 )


Floor no 9

0 10 20 30 40 50

Time (s)0 10 20 30 40 50

Time (s)0 10 20 30 40 50


minus03

00

03

Floor no 9

minus2minus1

0

1

2

Floor no 9

minus20

0

20


Floor no 9

Time (s)0 10 20 30 40 50

Time (s)0 10 20 30 40 50

Time (s)0 10 20 30 40 50

Disp

lace

men

t (m

)Ve

loci

ty (m

s)

Acce

lera

tion

(ms

2 )





lowast

119895can be

determined by

120577lowast

119895=

2120577119904119895120593119879

119895K119878120593119895+ 120578119863119895120593119879

119895K119863120593119895

2120593119879119895(K119878+ K119863)120593119895

(21)



119878and






0

2

4

6

8

10


Floo

r



0

2

4

6

8

10


Floo




Steel pipe

















Acknowledgments


References








































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

























Mx (119905) + Cx (119905) + Kx (119905) = P (119905) +Hu (119905) (17)





119865119889(119905 + Δ119905) = 119865

119889(119905) + 120572 sdot 119865

119889(119905) (

119889 (119905) = 0)

119865119889(119905 + Δ119905) = 119865

119889(119905) minus 120572 sdot 119865

119889(119905) (

119889 (119905) = 0)

(18)





0

1

2

3

4

5

6

7

8

9

Mas

s

00 02 04 06




0

1

2

3

4

5

6

7

8

9

Mas

s

00 02 04






119865119889(119905) =

min [119886119887119904 [119870119889(119909119887minus 119890)] minus 119865

0 119865max]

(119906 (119905) sdot 119906119891

(119905) gt 0

10038161003816100381610038161003816119906119891

(119905)

10038161003816100381610038161003816gt |119906 (119905)|)





119891



k = EAL

S e

uu



119906 (119905) =

119891119896

(119905) if 10038161003816100381610038161003816119891119896

(119905)

10038161003816100381610038161003816lt

10038161003816100381610038161003816119891119889

(119905)

10038161003816100381610038161003816(sticking)

119891119889

(119905) if 10038161003816100381610038161003816119891119896

(119905)

10038161003816100381610038161003816ge

10038161003816100381610038161003816119891119889

(119905)

10038161003816100381610038161003816(slipping)

119891119896

(119905) = 119896119889

[119889 (119905) minus 119890 (119905)]

(20)






minus06

00

06

Time (s)

Disp

lace

men

t (m

)Ve

loci

ty (m

s)

Floor no 9

minus4minus2

0

2

4

Floor no 9

minus60minus30

03060

Acce

lera

tion

(ms

2 )


Floor no 9

0 10 20 30 40 50

Time (s)0 10 20 30 40 50

Time (s)0 10 20 30 40 50


minus03

00

03

Floor no 9

minus2minus1

0

1

2

Floor no 9

minus20

0

20


Floor no 9

Time (s)0 10 20 30 40 50

Time (s)0 10 20 30 40 50

Time (s)0 10 20 30 40 50

Disp

lace

men

t (m

)Ve

loci

ty (m

s)

Acce

lera

tion

(ms

2 )





lowast

119895can be

determined by

120577lowast

119895=

2120577119904119895120593119879

119895K119878120593119895+ 120578119863119895120593119879

119895K119863120593119895

2120593119879119895(K119878+ K119863)120593119895

(21)



119878and






0

2

4

6

8

10


Floo

r



0

2

4

6

8

10


Floo




Steel pipe

















Acknowledgments


References








































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation















Mx (119905) + Cx (119905) + Kx (119905) = P (119905) +Hu (119905) (17)





119865119889(119905 + Δ119905) = 119865

119889(119905) + 120572 sdot 119865

119889(119905) (

119889 (119905) = 0)

119865119889(119905 + Δ119905) = 119865

119889(119905) minus 120572 sdot 119865

119889(119905) (

119889 (119905) = 0)

(18)





0

1

2

3

4

5

6

7

8

9

Mas

s

00 02 04 06




0

1

2

3

4

5

6

7

8

9

Mas

s

00 02 04






119865119889(119905) =

min [119886119887119904 [119870119889(119909119887minus 119890)] minus 119865

0 119865max]

(119906 (119905) sdot 119906119891

(119905) gt 0

10038161003816100381610038161003816119906119891

(119905)

10038161003816100381610038161003816gt |119906 (119905)|)





119891



k = EAL

S e

uu



119906 (119905) =

119891119896

(119905) if 10038161003816100381610038161003816119891119896

(119905)

10038161003816100381610038161003816lt

10038161003816100381610038161003816119891119889

(119905)

10038161003816100381610038161003816(sticking)

119891119889

(119905) if 10038161003816100381610038161003816119891119896

(119905)

10038161003816100381610038161003816ge

10038161003816100381610038161003816119891119889

(119905)

10038161003816100381610038161003816(slipping)

119891119896

(119905) = 119896119889

[119889 (119905) minus 119890 (119905)]

(20)






minus06

00

06

Time (s)

Disp

lace

men

t (m

)Ve

loci

ty (m

s)

Floor no 9

minus4minus2

0

2

4

Floor no 9

minus60minus30

03060

Acce

lera

tion

(ms

2 )


Floor no 9

0 10 20 30 40 50

Time (s)0 10 20 30 40 50

Time (s)0 10 20 30 40 50


minus03

00

03

Floor no 9

minus2minus1

0

1

2

Floor no 9

minus20

0

20


Floor no 9

Time (s)0 10 20 30 40 50

Time (s)0 10 20 30 40 50

Time (s)0 10 20 30 40 50

Disp

lace

men

t (m

)Ve

loci

ty (m

s)

Acce

lera

tion

(ms

2 )





lowast

119895can be

determined by

120577lowast

119895=

2120577119904119895120593119879

119895K119878120593119895+ 120578119863119895120593119879

119895K119863120593119895

2120593119879119895(K119878+ K119863)120593119895

(21)



119878and






0

2

4

6

8

10


Floo

r



0

2

4

6

8

10


Floo




Steel pipe

















Acknowledgments


References








































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

1

2

3

4

5

6

7

8

9

Mas

s

00 02 04 06




0

1

2

3

4

5

6

7

8

9

Mas

s

00 02 04






119865119889(119905) =

min [119886119887119904 [119870119889(119909119887minus 119890)] minus 119865

0 119865max]

(119906 (119905) sdot 119906119891

(119905) gt 0

10038161003816100381610038161003816119906119891

(119905)

10038161003816100381610038161003816gt |119906 (119905)|)





119891



k = EAL

S e

uu



119906 (119905) =

119891119896

(119905) if 10038161003816100381610038161003816119891119896

(119905)

10038161003816100381610038161003816lt

10038161003816100381610038161003816119891119889

(119905)

10038161003816100381610038161003816(sticking)

119891119889

(119905) if 10038161003816100381610038161003816119891119896

(119905)

10038161003816100381610038161003816ge

10038161003816100381610038161003816119891119889

(119905)

10038161003816100381610038161003816(slipping)

119891119896

(119905) = 119896119889

[119889 (119905) minus 119890 (119905)]

(20)






minus06

00

06

Time (s)

Disp

lace

men

t (m

)Ve

loci

ty (m

s)

Floor no 9

minus4minus2

0

2

4

Floor no 9

minus60minus30

03060

Acce

lera

tion

(ms

2 )


Floor no 9

0 10 20 30 40 50

Time (s)0 10 20 30 40 50

Time (s)0 10 20 30 40 50


minus03

00

03

Floor no 9

minus2minus1

0

1

2

Floor no 9

minus20

0

20


Floor no 9

Time (s)0 10 20 30 40 50

Time (s)0 10 20 30 40 50

Time (s)0 10 20 30 40 50

Disp

lace

men

t (m

)Ve

loci

ty (m

s)

Acce

lera

tion

(ms

2 )





lowast

119895can be

determined by

120577lowast

119895=

2120577119904119895120593119879

119895K119878120593119895+ 120578119863119895120593119879

119895K119863120593119895

2120593119879119895(K119878+ K119863)120593119895

(21)



119878and






0

2

4

6

8

10


Floo

r



0

2

4

6

8

10


Floo




Steel pipe

















Acknowledgments


References








































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










minus06

00

06

Time (s)

Disp

lace

men

t (m

)Ve

loci

ty (m

s)

Floor no 9

minus4minus2

0

2

4

Floor no 9

minus60minus30

03060

Acce

lera

tion

(ms

2 )


Floor no 9

0 10 20 30 40 50

Time (s)0 10 20 30 40 50

Time (s)0 10 20 30 40 50


minus03

00

03

Floor no 9

minus2minus1

0

1

2

Floor no 9

minus20

0

20


Floor no 9

Time (s)0 10 20 30 40 50

Time (s)0 10 20 30 40 50

Time (s)0 10 20 30 40 50

Disp

lace

men

t (m

)Ve

loci

ty (m

s)

Acce

lera

tion

(ms

2 )





lowast

119895can be

determined by

120577lowast

119895=

2120577119904119895120593119879

119895K119878120593119895+ 120578119863119895120593119879

119895K119863120593119895

2120593119879119895(K119878+ K119863)120593119895

(21)



119878and






0

2

4

6

8

10


Floo

r



0

2

4

6

8

10


Floo




Steel pipe

















Acknowledgments


References








































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

2

4

6

8

10


Floo

r



0

2

4

6

8

10


Floo




Steel pipe

















Acknowledgments


References








































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation



















Acknowledgments


References








































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation



































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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Review Article Dynamic Responses and Vibration Control of ...downloads.hindawi.com/journals/tswj/2014/538457.pdfReview Article Dynamic Responses and Vibration Control of the Transmission