Dynamic Responses and Vibration Control of the Transmission

8/12/2019 Dynamic Responses and Vibration Control of the Transmission

1/21

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

Bo Chen,1Wei-hua Guo,1 Peng-yun Li,2 and Wen-ping Xie2

Key Laboratory o Roadway Bridge and Structural Engineering, Wuhan University o echnology, P.O. Box ,No. Luoshi Road, Wuhan , China

Guangdong Power Grid Corporation Co. Ltd., Guangzhou , China

Correspondence should be addressed to Bo Chen; [email protected]

Received April ; Accepted May ; Published July

Academic Editor: ing-Hua Yi

Copyright Bo Chen et al. Tis 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.

Tis paper presented an overview on the dynamic analysis and control o the transmission tower-line system in the past ortyyears. Te challenges and uture developing trends in the dynamic analysis and mitigation o the transmission tower-line systemunder dynamic excitations are also put orward. It also reviews the analytical models and approaches o the transmission tower,transmission lines, and transmission tower-line systems, respectively, which contain the theoretical model, nite element (FE)model and the equivalent model; shows the advances in wind responses o 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, respectively. Te vibration control o the transmission tower-line system is also reviewed, which includesthe magnetorheological dampers, riction dampers, tuned mass dampers, and pounding tuned mass dampers.

1. Introduction

Te degradation o civil engineering structures due to harshenvironment may lead to structural damage and ailure,associated with the events such as member racture, columnbuckling, and brace breakage [, ]. o be a kind o high-rise structure with small damping, overhead transmissiontower-line systems are critical inrastructure or electrical

power transmission and are used throughout the world [].ransmission tower-line systems are prone to the dynamicexcitation, such as wind, earthquake, and iced shedding. Assupporting structures o coupled tower-line systems, trans-mission towers have relatively complex structural geometriesand present obvious nonlinear vibration associated withexibility o transmission lines. In reality, there exists a stronginteraction between the motion o the truss tower and that othe transmission lines subjected to dynamic loading, each owhich has requency-dependent stiffness properties, leadingto rathercomplex dynamic behaviour [].Teailureothetowers under dynamic loading hasbeen documented in manyliteratures [, ]. Tereore, it is relevant to assessthe dynamic

perormance o transmission tower-line systems consideringboth elastic and inelastic responses.

Te interest in the ability to monitor and mitigate thedynamic responses o the transmission tower-line systemis pervasive throughout the civil and electrical engineeringcommunities. o examine the properties o the coupledtransmission tower-line system, many theoretical and exper-imental investigations have been carried out during the past

two decades. With regard to the approaches and techniquesused or perormance evaluation and disaster mitigation,they can be classied 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 []. Te suggested designloads are commonly calibrated based on the assumptionthat the tower behaves elastically during dynamic excitation.In addition, the dynamic interaction between the towerand transmission lines cannot be taken into considerationduring the common design process. Tereore, this design

Hindawi Publishing Corporatione Scientific World JournalVolume 2014, Article ID 538457, 20 pageshttp://dx.doi.org/10.1155/2014/538457
http://dx.doi.org/10.1155/2014/538457http://dx.doi.org/10.1155/2014/538457


2/21

Te Scientic World Journal

approach does not provide deep insights into inelastic andnonlinear tower behaviour understrong dynamic excitations,even though the consideration o inelastic responses canbe important []. Furthermore, the primary environmentalload considered in the design o transmission structures isthe wind load, although the ice load may govern the design

o transmission tower-line systems in some cold regions.Tereore, the damage and ailure o transmission tower-linesystems have been requently reported across the world, eventhough the towersare designed andconstructed strictly basedon the specications and codes.

Afer that, the development and application o struc-tural assessment and mitigation approaches or transmissiontower-line systems in the elds o civil and electrical engi-neering have attracted more and more attention. o over-come the shortcomings o conventional approaches, manyanalytical models and approaches have been proposed anddeveloped or transmission tower-line systems in recent yearswith the aid o various techniques such as wind engineering,earthquake engineering, structural health monitoring, and

vibration control. However, there are still many challengesand difficulties in the perormance evaluation and vibrationcontrol techniques or the practical application o trans-mission tower-line system in various service conditions.Tereore, it is still essential to investigate the easibility,

validity, and applicability o the perormance assessment andcontrol approaches o the transmission tower-line systems.

Tis paper reviews the dynamic responses and control othe transmission tower-line system in the last two decades.Te challenges and uture trends in the disaster monitor-ing and mitigation o the transmission tower-line systemsubjected to dynamic excitations are also put orward. Testructure o the rest o the paper is as ollows. Section reviews the analytical models o transmission lines, trusstowers, and the coupled tower-line system, which containsthe theoretical model, nite element (FE) model, and theequivalent model; Section reviews the wind responseso the transmission tower-line system, which contains thestructural perormance subjected to various wind loadings,such as common winds, tornado, downburst, and typhoon,respectively, and the experiment and eld testing on windeffects; Sections and discuss the seismic responses andice-induced responses o the transmission tower-line system,respectively. Te vibration control o the transmission tower-line system is also reviewed. Finally, the challenges anduture trends in the dynamic assessment and mitigation

o transmission tower-line system are summarized in theconclusions.

2. Model of Transmission Tower-Line System

.. Model o ransmission Line

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

o various numerical simulating approaches. Based on theconclusions provided by Irvine [], the natural requencieso a transmission line or antisymmetric in-plane vibrationcan be expressed as

=2

( = 1, 2, 3, . . .) .

()

Te natural requencies o a transmission line or the sym-metric in-plane vibration can be determined by solving theollowing equations:

2=2

42

2

2; = /; 2 =

2

3 , ()where is the tensile orce o a transmission line;is themass o a transmission line per meter; and are the Youngmodulus and sectional area o a transmission line; is thehorizontal span o a transmissionline. In addition, the natural

requencies o a cable or out-o-plane vibrationVareV=

, ( = 1, 2, 3, . . .) . ()

() FE Model.A transmission line can be modelled by usingcable elements in the FE method []. Te equilibriumequation o theth cable element can be established by usingthe virtual work principle based on the nonlinear FE method.

Te strain matrix o the th cable elementB() isthesumo thelinear strain matrix B() and the nonlinear strain matrixB

()NL:

B()

=B

()

+B

()NL

. ()

Both the linear strain matrix B() and the nonlinear strain

matrix B()NL relate to the shape unction o a certain cable

element. Te stiffness matrix o theth cable element K() inthe global coordinate system (GCS) can be expressed as the

sum o the elastic stiffness matrix K() , displacement stiffness

matrix K() , and the stress stiffness matrix K() . Consider

K() = K()+ K()+ K(). ()

Te elastic stiffness matrix K() can be constructed only by

the linear strain matrix B() , while the displacement stiffness

matrixK() can be constructed by both thelinearstrain matrix

B() and nonlinear strain matrix B

()NL. Te stress stiffness

matrix K() is constructed by using the shape unction othe cable element and the element stress. Te globalstiffness matrix o a transmission line can be determined bycombining all the element stiffness matrices in the GCS:

K= =1

K(), ()

where denotes the number o all the cable elements in atransmission line. Te mass matrix o the transmission line


3/21


l l

v

u

ll l ll

1

2 3 4 56

7h7

h6h5

h1h2

h3

(a)

m1

m2

m3

L1

L2

L3

(b)

F : MDOF elastic model o a transmission line. (a) In-plane vibration. (b) Out-o-plane vibration.

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

M= =1

M(). ()

() MDOF Equivalent Model. Te transmission line can besimulated as several lumped masses connected with elasticelements as shown in Figure , which is the MDOF equivalentmodel. Te Hamilton variational statement o dynamicsindicates that the sum o the time variations o the differencein kinetic and potential energies and the work done by thenonconservative orces over any time interval1 to2equalszero []. Te application o this principle can lead directly tothe equation o motion o a transmission line:

21

line() line() + 2

1

line() = 0, ()in which

()and

()are the kinetic energy and potential

energy o a transmission line. line()equals the virtual workdone by the nonconservative orces on a transmission line.It is clear that the transmission line may vibrate around itsbalanceable position when it is subjected to the externaldisturbance. Te generalized coordinateo a transmissionline, namely,and, can be dened as the difference o theangleand length, respectively, as ollows:

= = 0,= = 0 , ()

where0is the original value oor the th element, 0and

are the original length and current length o the

th element,

respectively, and is the static deormation due to the gravityo theth element.Te equation o motion o an N-DOF transmission line

canbe derived directly rom the Hamiltonequation by simplyexpressing the total kinetic energyline, the total potentialenergyline, and the total virtual workline in terms o aset o generalized coordinates, namely, and. Ten,introducing the expression into the Hamilton equation andcompleting the variation o the rst term yield the Lagrangeequations o a transmission line as ollows:

line

line

+line

= , ()

whereis the generalized orcing unction o the transmis-sion line corresponding to the generalized coordinates.

Afer establishing the kinetic energy and potential energyo transmission line, the mass and stiffness matrices canbe determined through partial differential calculation o thegeneralized velocity and generalized displacement, respec-

tively. Te mass matrix o a transmission line or the in-planevibrationMin can be deduced by computing partial differen-

tial o the derivative o generalized coordinates/ and/, respectively. Te stiffness matrix o a transmissionline or the in-plane vibration Kin can be determined bycomputing partial differential o the generalized coordinates/ and/, respectively. In addition, the transmis-sionlinecan be simplied as a hanging line with a ew lumpedmasses when considering the out-o-plane vibration. Temass matrix Mout and stiffness matrix K

out o transmission

line can be deduced in the same way.

.. Model o ransmission ower

() FE Model. Te transmission tower is a typical spatialstructure constructed by using steel members, which can bemodelled by using beam and truss elements based on the FE

method. Te element stiffness matrix K() and mass matrixM

() o theth element in the GCS can be determinedby transorming the element stiffness matrix K() and mass

matrixM() in the local coordinate system (LCS) with the aid

o coordinate transormation matrix T() :

K() = T() K() T() ,

M() = T() M() T() .

()

Afer determining the element stiffness and mass matricesunder the GCS, one can construct the position matrix

o element reedom T() ollowing the FEM connectioninormation o each element under both local and globalcoordinate systems. Tus, the global stiffness matrix K andmass matrix M o a transmission tower in the GCS can beexpressed as

K= =1

T()

K()T

(),

M= =1

T()

M()T

(),()


4/21


(a)

15.000

29.500

55.500

43.000

98.000

76.500

66.500

88.500

122.000

110.000

(b)

F : Analytical model o a transmission tower. (a) D FE mode. (b) D model.

where is the total element number o the nite elementmodel o a transmission tower and T() is the reedomtransorm matrix rom element coordinate system to theGCS, which is the product o coordinate transormation

matrix T() and position matrix T() o theth element.

() D Lumped Mass Model.I a D nite element dynamicmodel is used to model a tower with many transmissionlines, the numerical step-by-step integration in the timedomain to determine dynamic responses o the tower-linecoupled system will be very time-consuming, which makesit impractical or parametric study and vibration controlinvestigation. Te dynamic excitation on the tower such aswind loads and earthquakes can usually be modeled as astationary or nonstationary stochastic process in time andnonhomogeneous in space.Te digital simulation o dynamicloading o a D nite element model o the transmissiontower-line system with the aid o the spectral representationmethod [,] may need enormous computation effort. othis end, a D lumped mass model is commonly used in prac-tice to investigate the wind/earthquake-induced dynamicresponse o a complicated transmission tower-line system[] (seeFigure ).

When a D FE dynamic model o a transmission toweris reduced to a D lumped mass model, some assumptionsare commonly adopted. Firstly, the mass o the transmissiontower, including the masses o all structural components andall nonstructural components and all equipment in the tower,is concentrated at several oors only. Ten, the average o thedisplacements o all nodes at a given oor in one commondirection is dened as the nominal displacement o that oorin that direction. Finally, only the horizontal dynamic loadingand responses are considered.

With these assumptions, the number o dynamic degreeso reedom o a transmission tower in the lumped massmodel is the number o oors selected. Te mass matrix

M o the lumped mass model is a diagonal matrix. Testiffness matrix K o the lumped mass model o degreeso reedom can be obtained based on the D FE model o thetransmission tower by taking the ollowing steps: () apply thesame horizontal orce at each node at theth oor such thatthe sum o all orces equals ; () determine the horizontaldisplacement o each node at theth oor and dene thenominal displacement o theth oor to have the exibilitycoefficient(, = 1,2 , . . . , ); () orm the exibilitymatrix F o

dimension; () inverse the exibility matrix

to obtain the stiffness matrix K.

.. Model o ransmission ower-Line System

() FE Model. Similar to the construction process o atransmission tower, the global stiffness andmass matrices o atransmission tower-line system in the GCS can be establishedby combining the stiffness and mass matrices o towers andlines in the GCS by using the FE method:

K= tower=1

K()+

line=1

K()

,

M= tower=1

M()+

line=1

M()

,

()

wheretower andline are the numbers o towers andtransmission lines in a transmission tower-line system,respectively.

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


5/21


Mn Mn

M1

M2

M3

M1

M2

M3

.

.

.

.

.

.

.

.

.

.

.

.

(a)

Mn

M1

M2

M3m1

m1

m2

m2

m3

m3

.

..

.

.

.

(b)

F : Analytical model o a transmission tower-line system. (a) In-plane vibration. (b) Out-o-plane vibration.

the transmission tower-line system can be developed by

combining the D tower model and the equivalent linemodel.

For the transmission tower-line system, the kineticenergy can be expressed in terms o the generalized coordi-nates and their rst time derivatives, and the potential energycan be expressed in terms o the generalized coordinatesalone. In addition, the virtual work which is perormed bythe nonconservative orces as they act through the virtualdisplacements caused by an arbitrary set o variations in thegeneralized coordinates can be expressed as a linear unctiono those variations. In mathematical terms the above threestatements are expressed in the orm

= 1, 2, . . . , , 1, 2, . . . , , = 1, 2, . . . , ,

= 11+ 22+ + ,()

where the coefficients1, 2, . . . , , are the general-ized orcing unctions corresponding to the coordinates1, 2, . . . , , respectively.

Te analytical model o transmission tower-line systemis displayed inFigure . Te kinetic energy and potentialenergyo the coupled system are

= tower=1

() +line

=1

() ,

= tower=1

()+ line

=1

() .

()

By substituting () into the Lagrange equation, the motiono equation o a transmission tower-line system can be deter-mined by computing the partial differential o the kineticenergy and potential energy to generalize coordinatesand their rst time derivatives.

3. Wind Responses of

Transmission Tower-Line System

ransmission tower connected by many lines has morecomplex structural geometries and behaviour than commonsel-supported towers. ransmission tower-line system isa typical wind sensitive structure and wind loading ofencontrols the structural design o transmission tower-linesystem [, ]. Te responseo structures to wind action mayinvolve a wide range o structural actions, including resultantorces, bending moments, cable tensions, and deectionsand acceleration. Te transmission lines, being relativelyslack under dead load, together with the behaviour o thetower and the conductors make the system very nonlinear.

It was considered that since time history analysis takes intoaccount nonlinearity this analysis is more accurate than themultimodal spectral analysis.

.. Perormance Subjected to Common Wind Loading. Earlystudies on guyed towers or transmission lines were ocusedon the galloping phenomenon [,]. Later works on thedynamic wind loading or transmission tower-line system,or example, the studies o Yasui et al. [] and Battistaet al. [], did not involve exible-type structures such asguyed towers. Liew and Norville [] presented a methodor studying the response o a transmission tower struc-tural system subjected to wind loads. Te wind speedsand the loads rom the conductors were considered as

the loadings on the transmission tower structural system.Te data were used to determine the requency responseunctions o the transmission tower structural system whichprovided a measure o response. Yasui et al. [] describeda method or analyzing wind-induced vibrations o powertransmission towers coupled with power lines. Tey alsodiscussed the inuence on the response characteristics odifferences in transmission support systems and the differ-ences between peak actors, computed rom a time seriesand rom the power spectrum density. Battista et al. []proposed a new analytical-numerical modelling or thestructural analysis o transmission line towers under windaction or stability assessment in a design stage. A simplied


6/21


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

F : Load patterns or perormance analysis o transmission tower: (a) rectangular, (b) inverted triangular, (c) rst mode, (d) powerlaw, and (e) tornado.

two-degree-o-reedom analytical model is also presentedand shown to be a useul tool or evaluating the systemundamental requency in early design stages. Loredo-Souzaand Davenport [] examined the inuence o the designmethodology in the response o transmission towers to windloading. Te Davenport gust response actor was comparedwith the statistical method using inuence lines. From theresults it can be concluded that the incorporation o thedynamic properties o transmission structures in the designmethodologies is neededand that the statistical method usinginuence lines is a more correct approach since it allowsor the inclusion o a larger number o actors in the designmethodology.

Te transmission tower-line systems become importantinrastructures in modern societies and their wind-inducedresponses are an essential and practical task in the saetyassessment. Okamura et al. [] carried outthe wind responseanalysis o a transmission tower in a mountainous area basedon ull-scale measurements. Te wind response analysisresults or the blowdown ow on the leeward slope o themountain corresponded closely with the measurements. Teanalytical results demonstrate that the evaluation o the blow-down angle is also important in the wind response analysis othe transmission tower in the mountainous area. Liu and Li[] presented an analytical ramework to evaluate the along-wind-induced dynamic responses o a transmission tower.wo analytical models and a new method were developed.One was a higher mode generalized orce spectrum model othe transmission tower and the other was an analytical modelthat includes the contributions o the higher modes derived

as a rational algebraic ormula to estimate the structuraldisplacement response. A new approach was developed byapplying load with displacement (ALD) instead o orceto solve the internal orce o transmission tower. It wasound that the ALD method can avoid calculating equivalentstatic wind loads compared with conventional methods. Teimportance o the dynamic response o guyed towers ortransmission lines under wind loading was evaluated byGani and Legeron []. Te research objective was to veriyi the simplied static-equivalent approach provided in thecurrent transmission line codes is sufficient or this typeo exible tower. It was ound that the static-equivalentapproach may underestimate the possible dynamic response.

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

Te numerical simulation o transmission tower-linesystems progressive collapse perormance is considered asa major research hotspot and signicant project, due tothe increasing number o wind-induced collapse accidentsrecently. o assess the collapse risk o transmission line struc-tures subject to natural hazards, it is important to identiywhat hazard may cause the structural collapse. Zhang andLi [] introduced a new method termed as the probabilitydensity evolution method (PDEM) so as to accurately com-pute the dynamic response and reliability o a transmissiontower. Te random parameters o the wind stochastic eld,such as the roughness length, the mean wind velocity, and theprobability density unctions, were investigated. It was oundthat not only the statistic quantities o the dynamic response,but also the instantaneous probability density unction o theresponse and the time-varying reliability can be determinedbased on the proposed method. Te results demonstratedthatthe PDEM is easible and efficient in the dynamic responseand reliability analysis o wind-excited transmission towers.

Banik et al. [] assessed capacity curves or transmissionline towers under wind loading. Te assessment was per-ormed by using a nonlinear static pushover (NSP) analysisand incremental dynamic analysis (IDA) using different loadpatterns as shown inFigure . For the IDA, temporally andspatially varying wind speeds were simulated based on powerspectral density and coherence unctions. Numerical resultsindicated that the structural capacity curves o the towerdetermined rom the NSP analysis dependon the load pattern

and that the curves determined rom the nonlinear staticpushover analysis were similar to those obtained rom IDA.Furthermore, Mara and Hong [] investigated the inelasticresponse o a sel-supported transmission tower under differ-ent wind events, including traditional atmospheric boundarylayer wind and downburst wind, and or wind loading atdifferent directions relative to the tower. Te NSP analysiswas used to obtain the capacity curve o the tower, dened bythe orce-deormation relationship, at each considered winddirection. Te results indicated that the yield and maximumcapacities vary with wind direction.

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


7/21


and stability analysis. A long-span transmission tower-linesystem in China with a span o m was taken as thereal example. Nonlinear buckling analysis or both the towerand tower-line systems was perormed to determine thecritical wind loads. Numerical results indicated that modalrequencies o low order modes decrease when the wind

velocity increases beore the structural instability happens inboth cases. Tereore, or the structural health monitoringo transmission lines, requency decrease o low order modeis a useul indicator to predict the happening o struc-tural instability. Zhang et al. [] examined wind-inducedcollapsed perormance o a transmission tower-line systemthrough numerical simulation. Te nite element models orthe single tower and transmission tower-line system wereestablished to simulate wind-induced progressive collapse byusing birth-to-death element technique with the aid o thecommercial package ABAQUS. It is demonstrated that thecollapse mechanism o the transmission tower-line systemdepended on the number, position, and last deormation odamage elements.

Galloping o overhead transmission lines has been underinvestigation or a long time in the industrial aerodynamicseld and is still awaiting solution. It is important to under-stand the effectso wind turbulence on galloping andto estab-lish an evaluation method or galloping o transmission linein gusty wind. Ohkuma and Marukawa [] investigated thegalloping o overhead transmission lines in gusty wind. Teydiscussed the differences between galloping in smooth windand galloping in gusty wind through a numerical simulationocusing on their behavior rather than their mechanisms. Inaddition, Verma and Hagedorn [] developed a modiedapproach o the energy balance principle by taking intoaccount in-span damping (Figure ). Te complex transcen-dental eigenvalue problem was solved or the conductor within-span ttings. With the determined complex eigenvaluesand eigenunctions, a modied energy balance principle wasthen used or scaling the amplitudes o vibrations at eachresonance requency. Bending strains are then estimated atthe critical points o the conductor.

.. Perormance Subjected to ornado. A thunderstorm, alsoknown as an electrical storm, a lightning storm, thunder-shower, or simply a storm, is a orm o turbulent weathercharacterized by the presence o lightning and its acousticeffect on the Earths atmosphere known as thunder. Tun-derstorms are usually accompanied by strong winds, heavy

rain, and sometimes snow, sleet, hail, or no precipitationat all. Tere are several different types o thunderstorms,depending on the origin and the associated meteorologi-cal activities. All types o thunderstorms can occasionallybecome severe. Te most severe thunderstorm is a tor-nado and another type o severe thunderstorm is the so-called downburst. In many countries, a large proportion oailures o 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 orthe risk assessment o transmission tower-line system isessential. However, a lack o appropriate stochastic models

x

N

T A EI

F : Schematic view o a typical long-span transmission line.

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

ornadoes contain the most powerul effects o all winds[]. A tornado consists o a vortex o air that develops withina severe thunderstorm and moves with respect to the groundwith speeds o the order o km/hr in a path. A tornado

is a violently rotating column o air that is in contact withboth the surace o the earth and the cumulonimbus cloud,which is ofen reerred to as twister or cyclone. ornadoesare observed as unnel-shaped clouds and the tangentialspeeds are probably highest at the unnel edge and drop-offtoward the center and with increasing distance outside theunnel. Since the centriugal orces in the tornado vertex arexceed the Coriolis orces, the latter may be neglected and thegradient wind equation can be expressed as

2=

1

, ()

where

is the cyclostrophic wind velocity,

is the radial

distance rom the center o the vortex, is the air density, andthe / is the pressure gradient along the radius. A tornadois different to downburst and microburst. In a tornado,high velocity winds circle a central point, moving inwardand upward, whereas in a downburst the wind is directeddownward and then outward rom the surace landing point.Many transmission line and tower ailures worldwide areattributed to high intensity winds associated with tornadoes.

Savory et al. [] described models or the wind velocitytime histories o transient tornado and microburst eventsand the resulting loads on a lattice transmission tower.A dynamic structural analysis was developed to predict atornado-induced shear ailure. Te results rom the predic-

tions were encouraging in that the tornado ailure appearedto concur well with evidence rom the eld, whilst the effecto the microburst was clearly less severe. Hamada et al. [ ]developed a numerical scheme to assess the perormanceo transmission lines under tornado wind load events. Tewind orces associated with these tornado elds were eval-uated and later incorporated into a nonlinear nite elementthree-dimensional model or the transmission line system.A comparison was carried out between the orces in themembers resulting rom the tornadoes and those obtainedusing the conventional design wind loads. Te study revealedthe importance o considering tornadoes when designingtransmission line structures.


8/21


Ground

(a) Ring vortex model

Ground

(b) Wall jet model

F : ypical models o downburst.

: ypes o thunderstorm winds in Australia.

ype Horizontal scale Duration

Microburst kilometers minutes

Macroburst kilometers minutes

Outows(gust ronts, squall lines)

kilometers hours

Ahmed et al. [] carried out the collapse and pull-downanalysis o high voltage electricity transmission towers sub-

jected to cyclonic wind. Tey presented a novel methodologydeveloped or the critical inrastructure protection modellingand analysis (CIPMA) capability or assessing local windspeeds and the likelihood o tower ailure or a range otransmission tower and conductor types. Similar work wasconducted by Pecin et al. [] to evaluate the mechanicalglobal actions due to an approximate mathematical model oa tornado. Usage o tornadic response spectrum practices wasproposed and particular aspects o tornadic loads on towerstructures were analyzed.

.. Perormance Subjected to Downburst. A downburst is astrong ground-level wind system that emanates rom a singlesource, blowing in a straight line in all directions rom thatsource. Downbursts are created by an area o signicant rain-cooled air that afer reaching ground level spreads out inall directions producing strong winds. Downbursts includemicrobursts and macrobursts []. Microbursts are smallerand more concentrated than downbursts, the physical size o

which is about km or less in horizontal extent. A macroburstis a large downburst. Te physical size o thunderstormactivities in Australia is shown inable []. Downburstscan induce an outburst o damaging winds near the ground,with near surace speeds in excess o m/s. During thepast decade, many electrical transmission tower structureshave ailed during downburst. Te nature o the loadingimposed on a transmission tower by a downburst will dependupon the stage o the development o the event when itinteracts with the tower []. I the downburst is close to theground and approaching touchdown, then there may wellbe a signicant vertical loading component on the tower.However, i the microburst has already reached the ground

and is spreading outward as it impinges upon the tower,then the main loading components will be in the horizontalplane.Tere are essentially two orms o simplied modelsorthe wind eld associated with a downburst [,], namely,the ring vortex model and the impinging wall jet model, asillustrated schematically inFigure . Many studies have beenperormed to understand the behavior o transmission tower-line system under such localized wind events.

Shehata et al. [] assessed the effects o varying thedownburst parameters on the perormance o a transmissionline structureby taking several real towers as examples, whichwere ailed in Manitoba, Canada, during a downburst eventin . Te spatial and time variation o the downburst windeld was examined. Ten, the variations o the tower mem-bers internal orces with the downburst parameters werediscussed. In addition, the structural behavior under criticaldownburst congurations was compared to that resulting

rom the boundary layer normal wind load conditions.Furthermore, they [,] perormed the ailure analysis oa transmission tower that collapsed in Winnipeg, Canada,subjected to a microburst event. Teir study was conductedusing a uid-structure numerical model that was developedin-house. Te model was employed rst to determine themicroburst parameters that are likely to initiate ailure o anumber o critical members o the tower. Progressive ailureanalysis o the tower was then conducted by applying theloads associated with those critical congurations.

Darwish et al. [] assessed the dynamic characteristicsand behavior o transmission line conductors under theturbulent downburst loading. A nonlinear numerical model

was developed and used to predict the natural requenciesand mode shapes o conductors at various loading stages.Dynamic analysis was carried out using various down-burst congurations. Te made observations indicated thatthe responses are affected by the background component,while their sonant component turns to be negligible duelarge aerodynamic damping o the conductors. Darwishand Damatty [] also investigated the behavior o sel-supported transmission line towers under downburst load-ing. A parametric study was perormed to determine thecritical downburst congurations causing maximum axialorces or various members o a tower. Te sensitivity othe internal orces developing in the tower members to


9/21


changes in the downburst size and location was studied. Testructural behavior associated with the critical downburstcongurations was described and compared to the behaviorunder normal wind loads.

.. Perormance Subjected to yphoon. Te winds produced

by severe tropical cyclones also known as hurricanes andtyphoons are the most severe wind loading on earth.However, their inrequent occurrence at particular locationsofen makes the historical record o recorded wind speeds anunreliable predictor or design wind speeds. Bulk transmis-sion tower-line system is prone to strong typhoon loadings,particularly at the open coastal terrain in cyclonic regions.Te investigation on the perormance o the transmissiontower-line system subjected to typhoon is limited due to thedifficulties in collecting typhoon wind loading.

omokiyo et al. [] reported the typhoon damageanalysis o transmission towers in mountainous regions oKyushu, Japan. Tey have operated a network or wind

measurement, NeWMeK, which measures wind speed anddirection, covering these mountainous areas, segmenting theKyushu area into high density arrays since . In particular,they discussed the wind characteristics o yphoon Bart in and the damage to towers located in the mountainousregions along with the distribution and direction o allentrees. It was observed that transmission towers were damagedby winds that became stronger due to the effect o the localterrain or by being involved in changes in tensile orces o thetransmission lines o the towers that had already collapsed.Tese towers were collapsed due to a combination o theabove actors. Te world tallest transmission tower, the mZhoushan transmission towers over the typhoon-prone seastrait, was taken as an example by Huang et al. [] toexamine structural wind effects. ime domain computationalsimulation approach was also employed to predict dynamicresponses o the transmission tower and the displacementbased gust response actors (GRFs). Te air comparison ogust loading actors or GRFs was made between the results othe experimental approach and the computationalsimulationapproach, which was an effective alternative way or quicklyassessing dynamic wind load effectson high-riseand complextower structures.

.. Experiment and Field esting or Wind Effects

() Wind unnel est. Compared to the theoretical and

numerical investigation, the studies on the perormance otransmission tower-line system through experiments andeld measurement are quite limited. Vortex-induced vibra-tion is a critical problem or the steel cylinders used intubular towers, such as transmission towers. Tereore, Denget al. [] perormed vortex-induced vibration tests on lull-scale cylinders to study the vibration perormance o steeltubes connected with typical joints in transmission towers,including [-shaped gusset plate connection, U-shaped gussetplate connection, cross-gusset connection, and the ange(see Figure ). Te testing observations indicated that vortex-induced vibration can occur not only in laminar ows,but also in turbulent ows, and the amplitude decreases as

F : View o wind tunnel testing o the vortex-inducedvibration.

F : Scheme o the eld testing.

the turbulence intensity rises. In addition, Deng et al. []carried out the wind tunnel study on wind-induced vibra-tion responses o an ultra-high-voltage (UHV) transmissiontower-line system. A discrete stiffness method was appliedto design the aeroelastic model on the basis o similaritytheory as shown inFigure . Te dynamic characteristics othe single tower and the tower-line system were identiedand the displacement responses at different positions wereobtained under a variety o wind speeds. It was ound thatthe wind-induced vibration coefficient specied by the codeis much smaller than that by testing. Tus, the code valueseems to be unsae or the UHV transmission tower.

Strong winds are observed commonly associated withheavy rains. Te wind-rain-induced vibration and damageo civil engineering structures are requently reported, inparticular or cables and transmission lines. Li et al. []carried out the testing on wind-rain-induced vibration otransmission towers. Te aeroelastic models o the antelopehorn tower and pole tower were manuactured based onthe similarity theory or the wind tunnel tests. Te responseanalyses and experiments or the two kinds o models wereconducted under the wind-induced and wind-rain-inducedactions with the uniorm and turbulent ow. It was shownthat the results o wind-rain-induced responses were biggerthan those o only wind-induced responses.


10/21


F : Te monitored L transmission line tower.

() Field esting. Savory et al. [] discussed some o thendings arising rom long-term monitoring o the windeffects on a transmission tower located on an exposed site inSouth West England. Site wind speeds and oundation loadswere measured. Comparisons between the measured strainsand those determined based on UK code indicated that thecode overestimates most o the measured oundation loads bya moderate amount o about % at higher wind speeds. Tistends to conrm the validity o the code or assessing designoundation loads. Furthermore, Savory et al. [] presenteda comparison between the wind-induced oundation loadsmeasured on a type L transmission line tower (seeFigure )during a eld study in the UK and those computed using

the UK Code o Practice or lattice tower and transmissionline design. Te analysis demonstrated excellent agreementbetween the code calculations and the measured results.

Te galloping is commonly observed in the overheadtransmission line vibration during the ice storm. A methodo single channel signal processing was implemented byGurung et al. [] to discuss galloping o transmission linesbased on eld data. Ten, the same method was extendedby them [] to identiy and characterize several numberso vibrations observed in the suruga est Line o KansaiElectric Power Company during ice storms. Te piecewiseapplication o Pronys method was introduced to discuss

time-dependent characteristics o harmonic components inthe responses. Te existence o motion-induced orce wasthen conrmed or galloping events by introducing theusual buffeting theory. Based on ull-scale measurement data,akeuchi et al. [] reported on several aerodynamic damp-ingproperties o twotransmission towersunderconditions ostrong winds. Tey introduced a new method o estimatingdamping properties, which was applicable to the responserecord o a multidegree o reedom system such as thecoupled structure o a transmission tower and conductors.Te component o every vibration mode o the towers wasextracted rom a measured time history and the accuratedamping ratios were estimated individually (seeFigure ).

4. Seismic Responses of TransmissionTower-Line System

Te conventional seismic assessment o transmission towersis usually carried out by considering each tower as anindividual structure without taking the inertia coupling and

the strong traction o transmission lines into consideration.In addition, many o structural engineers were used to simplyignore the wire mass or to simpliy the transmission lines asa series o lumped masses affiliated to the tower in seismiccomputation. Up to now, the researches related to the seismicperormance o transmission tower-line systems are limited.o this end, Li et al. [] developed an analytical model orthe seismic analysis o the transmission tower-line system byconsidering the tower-line interaction. o veriy the validityo the proposed model, the shaking-table experiments o thecoupled tower-line system were carried out as displayed inFigure . Te results indicated that the errors o theoreticaland testing results o systemic seismic responses are withinthe acceptable range. Based on the made observations, asimplied analysis method was proposed to make the seismicresponse calculation o coupled system aster and moreeffective.

aniwaki andOhkubo [] developed an efficient optimalsynthesis method to determine the optimum solutionsor thestructural shape, cross-sectional dimensions, and materialtype o all member elements o large-scale transmissiontowers subjected to static and seismic loads. Te exampleo a cost-minimization problem or a real transmissiontower that considers not only the material costs, but alsothe cost o land as objective unctions was presented todemonstrate the rigorousness, efficiency, and reliability othe proposed method. Lei and Chien [] investigated the

dynamic behavior o transmission towers linked togetherthrough electrical lines when subjected to a strong groundmotion. Te transmission lines and the towers were modeledby using the cable elements and the D beam elements,respectively, both considering geometric nonlinearities. Testrength capacities and the racture occurrences or the mainmembers o the tower were examined with the employmento the appropriate strength interaction equations. Te madeobservation indicated that the ignorance o cable contribu-tion to total seismic responses, especially the portion causedby the cable mass, would induce signicant errors in predict-ing the ultimate strength o tower members. More recently,Wang et al. [] carried out the progressive collapse analysis

o the transmission tower-line system under earthquake withthe aid o the commercial package ABAQUS. Te collapsepaths and ailure positions o the power transmission towerwere obtained under different seismic excitations.

ian et al. [] studied the seismic responses o thetransmission tower-line system subjected to spatially vary-ing ground motions. Te towers were modeled by usingbeam elements and the transmission lines were modeled byusing cable elements considering the nonlinear geometry.Both the incoherency o seismic waves and wave traveleffects are taken into account. Te effects o boundaryconditions, ground motion spatial variations, incident angleo the seismic wave, coherency loss, and wave travel on


11/21


(a) ower A (b) ower B

F : Elevation o the example towers.

(a) Photograph o the model

x

y

LineM = 0.5 kg

M = 3 kg

M = 2 kg

M = 2 kg

M = 3 kg

(b) esting model

F : Elevation o testing model.

the system were investigated in detail. Te observationsdemonstrated that the uniorm ground motion at all thesupport o the system cannot provide the most critical caseor the response calculations o the transmission tower-line system. In addition, they [] examined the dynamicresponses o a transmission tower-line system at a canyonsite under spatially varying ground motions. Te spatially

varying ground motions were simulated stochastically based

on an empirical coherency loss unction and a ltered ajimi-Kanai power spectral density unction. It was ound thatneglecting motion spatial variations may lead to a substantialunderestimation o the responses o the transmission tower-line system during strong earthquakes. Furthermore, Li et al.[] analyzed the effects o multicomponent multisupportexcitations on the responses o a transmission tower-linesystem. Multicomponent and multisupport earthquake inputwaves were generated based on the code or the seismicdesign o electrical installations. An extensive parametricstudy was conducted to investigate the behavior o thetransmission tower-line system. Similar investigations wereconductedbyBaietal.[] to study the nonlinearresponses o

a transmission tower-line system on a heterogeneous site sub-jected to multicomponent spatially varying ground motions.Te made observations revealed that the multisupport andmulticomponent earthquake excitations with considerationo the site effects should be considered in a reliable seismicresponse analysis o the transmission tower-line system.

5. Ice-Induced Response of Transmission

Tower-Line System

emperature load is a typical environmental loading actingon the civil engineering structures, in particular in somecold regions []. 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 ). Shedding o the icethat accreted on transmission line cables is a common andpractical issue in cold regions across the world. Te allingo ice chunks may result in high-amplitude vibration o


12/21


F : Accreted ice o the transmission line section.

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

Jamaleddine et al. [] investigated the ice shedding roma two-span section using the commercial FE analysis sofwareADINA. Tey carried out a total o tests on a reduced-scale two-span model to study the effects o ice sheddingon overhead lines. Model predictions were validated on asmall-scale laboratory model. McClure et al. [,] studiedthe effects o ice thickness, partial shedding, and differentline parameters on the dynamic response o ice shedding ontransmission lines by a similar numerical approach. Jakse etal. [] developed a numerical model to examine the ice-shedding effects o a kV overhead power line in Slovenia.A single-span and three-span FE models o conductorswere established in the computation. Te made observationsdemonstrated that the deected line conguration and large-amplitude oscillations resulting rom load shedding wereproblematic. Te situation was corrected by the utility onsome line sections by installing interphase long insulatingrod spacers. Kalman et al. [] established a nonlinear FEmodel or ground wires by ADINA, and several ice-sheddingscenarios were studied with variables including span lengthand pulse-load characteristics. Kollar and Farzaneh []numerically examined the conductor vibration ollowing ice

shedding rom one subconductor in a bundle. Furthermore,they [] presented a different modeling approach to examinethe dynamic behavior o a spacer damper located at midspanin twin, triple, and quad bundles afer ice shedding.

Fengli et al. [,] investigated dynamic responses otransmission tower-line system under ice shedding. Te DFE model o 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 . Many actors were considered in the ice-sheddingsimulations suchas tower-line coupled effect,phase combina-tion o the ice-shedding conductors, thickness o the accreted

ice, length o the ice-shedding span, and elevation difference.Effects o different actors on the dynamic responses o jump-ing heights, loads at the end o insulators, and the orces otransmission tower were also studied. Te made observationindicated that stress ratios o members at the tower headunder design ice thickness exceed the permitted values under

a large intensity o ice shedding. In addition, Yang et al. []also analyzed the unbalanced orce o the transmission tower-line system in heavy icing areas. A seven-continuous-spanconductor-string model o transmission lines was developedto examine the effects o design parameters, which includedthe loading mode o accreted ice, the eccentricity o accretedice, the wind velocity, the ice thickness, the icing rate,the spanlength, the elevation difference, and the span difference.

Xie and Sun [] studied the ailure mechanism o trans-mission towers under ice loads and investigated the pertinentretrotting strategy or increasing the load-carrying capacityo the tower. An experimental study was conducted on twopairs o subassemblages o a typical kV transmissiontower o the same type as those suffered the most severedamage during the ice disaster in South China in (seeFigure ). Te mechanical behavior, ailure mode, strain, anddeormation at critical points o the specimens were studied.Te made observations revealed that buckling o the main legwas the predominant ailure mode o structures. It was oundthat the addition o the diaphragm signicantly improved themechanical perormance o transmission towers by reducingthe torsional effect on main members and inhibiting the out-o-plane deormation o diagonal braces.

Kollar and Farzaneh [] investigated the ice sheddingrom 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 o concentrated loads. Te experimentalsimulation was implemented by load shedding tests on asmall-scale laboratory model. Numerical model predictionswere validated by comparing them to observations obtainedrom experiments and ull-scale tests. Yang et al. [] carriedout the analysis o the dynamic responses o a prototypeline rom iced broken conductors. A ull-scale transmissionline section o three continuous spans was established andsteel cables were used to simulate the iced conductors byconsidering the equivalent mass o the accreted ice. Brokenconductor experiments were carried out or different types oconductors and ice thickness. ime histories o the tensionsand displacements at the middle o conductor spans were

measured. Te experimental results indicated that the impacteffect is more signicant or the location nearer to thebreak point. Te dynamic impact actors decrease with theincrease o the ice thickness, and the impact actors oconductors without accreted ice are much higher than thoseo conductors with accreted ice.

6. Vibration Control of TransmissionTower-Line System

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


13/21


(a) Initial accreted ice (b) Uniorm ice shedding (c) Nonuniorm shedding

F : Ice-shedding scenarios.

F : Failure phenomena o single-panel subassemblage with-out diaphragms.

while accepting a certain level o structural damage. An alter-native approach to prevent catastrophic damage o transmis-sion tower-line system is to install control devices. Currentstudies on the vibration mitigation o transmission tower-line systems ocus on the application o dynamic absorbersand energy-dissipating dampers. Different types o energy-dissipating dampers have been developed recently as analternative approach or dynamic mitigation o transmissiontower-line system. Te dampers can be manuactured as anaxial member to replace common structural members o atruss tower and, thus, it avoids the additional occupancyo structural space. Furthermore, passive and semiactivedampers can reduce dynamic responses o all mode shapes

o the transmission tower-line system. Figure displays atypical installation scheme o energy-dissipating dampers ina transmission tower.

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

Mx()+ Cx()+ Kx()= P ()+Hu () , ()whereM, C, and K are mass, damping, and stiffness matriceso the transmission tower-line system, respectively; x(),x()and x() are the displacement, velocity, and accelerationresponses with respect to the ground, respectively; P() isthe dynamic excitations; u

()is the orce provided by control

F : Installation scheme o energy-dissipating dampers ontransmission tower.

devices or suppressing dynamic vibration; and H is theinuence matrix or u().

Different types o semiactive devices can be developedto equip control devices with actively controlled parametersorming a semiactive yet stable and low-power consumingdamping system. Chen et al. [,] rstly proposed a novelapproach or the semiactive control o transmission tower-line system under dynamic excitations by using magne-torheological (MR) dampers. MR dampers are typical smart(semiactive) dampers and may overcome the shortcomingso dynamic absorbers because o their excellent controlperormance. A dynamic iteration process was developedor the numerical simulation o the dynamic responses o

the transmission tower-line system. wo semiactive controlstrategies were proposed or the vibration mitigation otower-line system. Te rst one was based on xed incremento controllable damper orce as expressed in

( + )= ()+ () , () =0 ,( + )= () () , ()= 0 ,

()

where() is the controllable Coulomb damping at timeinstant, is the increment coefficient o the dampingorce, and

() is the slipping velocity o MR damper at


14/21


0

1

2

3

4

5

6

7

8

9

Mass

0.0 0.2 0.4 0.6

Peak displacement (m)

Original structurePassive-off

Passive-on

Semi-active number 1Semi-active number 2

(a) In-plane vibration

0

1

2

3

4

5

6

7

8

9

Mass

0.0 0.2 0.4Peak displacement (m)

Original structurePassive-off

Passive-on

Semiactive number 1Semiactive number 2

(b) Out-o-plane vibration

F : Comparison o control perormance o peak displacement.

time instant. Te second one was a clipped-optimal strategybased on uzzy control principle as expressed in

()=min 0, max () ()> 0, ()>| ()|min (other cases) ,

()

where0 is a small adjustable quantity,max andmin arethe coulomb damper orces corresponding to themaxandmin, respectively, and() is the active control orcedetermined based on uzzy rules. A real transmission tower-line system constructed in Southern China was taken asan example to examine the easibility and reliability o theproposed control approach. In addition, a parametric study

was conducted in order to examine the effects o bracestiffness, wind loading intensity, and parameters o MRuids on the control perormance. Te results as shown inFigure demonstrate that the MR dampers can be utilizedon the wind-induced vibrationcontrol o transmission tower-line system because o its simple conguration as well asits satisactory energy-dissipating capacity i the damperparameters are optimally determined.

Chen et al. [] proposed an integrated approach torealize both the vibration control and the damage detectiono a transmission tower-line system subjected to seismicexcitation by using semiactive riction dampers as shown inFigure . Te semiactive control orce

()depends on either

k= EA/L

S,e

uu

F : Mechanical model o a semiactive riction damper.

the sticking or the slipping state o the damper and it can bewritten as [,]

()= { () , i ()


15/21


0.6

0.0

0.6

Time (s)

Displacement(m)

Velocity(m/s)

Floor no. 9

4

2

0

2

4

Floor no. 9

60

30

0

30

60

Acceleration(m/s2)

Original structure

Semi-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


0.3

0.0

0.3

Floor no. 9

2

1

0

1

2

Floor no. 9

20

0

20

Original structure

Semi-active number 1

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

Displacement(m)

Velocity(m/s)

Ac

celeration(m/s2)


F : Control perormance on top o the transmission tower.

the easibility and reliability o the proposed vibration controlapproach and damage detection approach. Figure indi-cated the control perormance on top o the transmission

tower. Te results demonstrated that the incorporation oriction dampers into the transmission tower-line system cansubstantially suppress the earthquake-induced responses othe transmission tower. Te damage size and location o thetransmission tower can be accurately identied even withnoise contamination.

In reality, conventional dynamic design o thetransmission-tower line system by using control devicesis quite complicated to be carried out by the commonstructural engineers. o this end, Chen et al. [] proposeda method or the wind-resistant design o the transmissiontower-line system by using viscoelastic dampers. Teequivalent damping ratio o the wind-excited transmission

tower incorporated with viscoelastic dampers can bedetermined by

=2 K+ K2K+ K , ()

whereis the critical damping ratio o theth mode shape,is theth mode shape o the controlled tower, and KandK are the stiffness matrices o the towerand thecontributionmatrix o viscoelastic dampers to the structural stiffnessmatrix.

Te practical method o the wind-resistant design wasdeveloped based on the Chinese design code. A real trans-mission tower-line system constructed in China was taken

as the example to examine the easibility and reliability othe proposed approach.Figure displays the displacementresponses o the transmission tower with/without viscoelasticdampers. Te observations demonstrated thatthe viscoelasticdampers can be utilized in the wind-resistant design otransmission tower-line system because o its simple congu-ration as well as satisactory control perormance. Te designmethod proposed canalso be applied to wind-resistant designo civil engineering structures installed with other energy-dissipating devices.

Another typical control device commonly utilized in civilengineering structures is the tuned mass damper (MD).MD can reduce the structural dynamic responses to some

extent, while it requires one or more large additional masses.Owing to the inherent nature o MD, it can only abate the

vibration o tuned mode shapes instead o the global dynamicresponses. ian et al. [] investigated the seismic controlo power transmission tower-line coupled system subjectedto multicomponent excitations. Te equation o motion oa transmission tower with MD under multicomponentexcitations was established. Te structural seismic responseswith geometric nonlinearity were computed in the timedomain. Te optimal design o the transmission tower-linesystem with MD was determined based on different massratio. Te effects o wave travel, coherency loss, and differentsite conditions on the system without and with control were


16/21


0

2

4

6

8

10

0.0 0.5 1.0Displacement (m)

Floor

Original structuresWith dampers


0

2

4

6

8

10

0.0 0.5 1.0Displacement (m)

Floor

Original structuresWith dampers


F : Displacement responses o the transmission tower with/without viscoelastic dampers.

Steel pipe

Mass block Viscoelastic material

F : Tree-dimensional diagram o a pounding MD.

examined, respectively. More recently, a new type o MD,the pounding tuned mass damper (PMD) as shown inFigure , was proposed by Zhang et al. [] to examine theseismic resistant perormance o a transmission tower. In thePMD, a limiting collar with viscoelastic material laced onthe inner rim is installed to restrict the stroke o the MDand to dissipate energy through collision. Te poundingorce is modeled based on the Hertz contact law, whereasthe pounding stiffness is estimated in a small-scale test. A m transmission tower was taken as the example to veriythe validity o the PMD through numerical simulation.Harmonic excitation and time-history analysis demonstratedthe PMD superiority over the traditional MD.

7. Concluding Remarks

An overview is presented in this study on research advancesin theanalysis o transmissiontower-line systems with special

emphasis laid upon the response assessment and vibrationcontrol. Te research activity going on around the worldin terms o wind-induced responses, seismic responses,ice effects, and vibration control is reviewed, respectively.It is addressed in this review that analytical approachesbased on the transmission tower-line system are promisingin comparison with traditional techniques. Te approaches

based 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. Te investiga-tion o the dynamic perormance and control approaches othe transmission tower-line systems is not over yet. Tere arestill difficulties in the researches and the main challenges anduture development trends are as ollows.

() Development and improvement o analytical modelso tower-line systems are still expected. From theview,it can be seen that recently there have been innovativeapplications and improvement o the analytical mod-

els. Many models or transmission lines have beenproposed to simulate the dynamic responses o theline in a more accurate and quick manner with thenonlinearity. Tereore, the analytical models o 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 orm morepowerul models or analyzing structural dynamicresponses. Tus, urther studies on analytical modelsare necessary and imperative or the assessment andcontrol o the linearand nonlineardynamic responseso tower-line systems.


17/21


() remendous eld measurement demonstrates thatthe wind loads acting on towers and lines are quitecomplicated, in particular in the regions close tocoastal areas. Te loading models and patterns or theextreme wind events, such as typhoon, downburst,and tornado, are quite different to that o common

monsoon winds. Upto now, the studies on the loadingmodels o transmission tower-line system subjectedto extreme winds are still very limited. Te damage,ailure, and collapse o transmission towers and lineshave been requently reported. Tereore, wind load-ing on transmission tower-line system is a practicalyet challenging issue that should be investigated indetail in the uture.

() Similar to that o the winds, the loading modelsand effects o other dynamic excitations such asearthquake and ice shedding still deserve urtherinvestigation. Te investigation o seismic damagesindicates that the dynamic interaction between the

truss tower and the soil may be intensive under strongearthquakes. Furthermore, the span o the transmis-sion line is quite large in comparison with commoncivil engineering structures. Tus, the multiexcitationeffects o the transmission tower-line system shouldbe taken into consideration in detail.

() ransmission lines with long span are prone to thegalloping under accumulated snow and ice, whichis an important actor to induce the cable ruptureand tower ailure. Te mechanism o galloping andinduced instability o the tower-line system is still notclear and the analytical models and approaches orthe evaluation on the dynamic stability o tower-linesystem should be urther examined.

() Te widely reported disasters o transmission tower-line systems around the world make it clear thatthe structures cannot avoid damage and ailureunder extreme loadings, such as typhoon, downburst,and strong earthquake, even though the system isdesigned based on the current specications andcodes. Te major reason is that the loading patternsspecied in the codes cannot depict the extreme load-ings and the design method is perormed based onstatic analysis instead o nonlinear dynamic analysison the interaction o tower-line systems. Accordingly,

reasonable methods or the perormance assessmento the transmission tower-line system deserve urtherinvestigation.

() Te experiment and eld measurement are consid-ered as a promising and powerul approach in theperormance assessment o transmission tower-linesystems. Comparative studies o testing observationswith those rom the theoretical computation andnumerical simulation are limited and needed to bemore conducted and addressed. It is ound that thetested dynamic properties o the transmission towerare commonly different to those based on the niteelement model. Tis is a practical yet difficult issue,

while the model updating methods o transmissiontower-line systems have not been reported. Tereore,effective model updating approaches are necessary toaccurately predict the structural responses.

It is clear that there still exist some shortcomings in the

perormance assessment and vibration control techniqueso the transmission tower-line system. Te benets o thecurrent technology ar outweigh the problems o not usingthem. Tis is evident by the tremendous amount o contribu-tions rom the scientic community or urther developingcorresponding novel technology in the real application otransmission tower-line systems. o this end, great effortsshould be taken to improve the analytical models andapproaches in the near urther. Te maniestation o theperormance assessment and vibration control technology otransmission tower-line systems is warmly expected.

Conflict of Interests

Te authors declare that there is no conict o interestsregarding the publication o this paper.

Acknowledgments

Te authors are grateul or the nancial support romthe technological project o the Chinese Southern PowerGrid Co. Ltd (Grant K-GD-), the National NaturalScience Foundation o China (Grant ), the FokYing-ong Education Foundation (Grant ), and theFundamental Research Funds or the Central Universities(WU, -II-).

References

[] B. Chen, Y. L. Xu, and W. L. Qu, Evaluation o atmosphericcorrosion damage to steel space structures in coastal areas,International Journal o Solids and Structures, vol. , no. -,pp. , .

[] B. Chen and Y. L. Xu, A new damage index or detectingsudden change o structural stiffness, Structural Engineeringand Mechanics, vol. , no. , pp. , .

[] H.-F. Bai, .-H. Yi, H.-N. Li, and L. Ren, Multisensors on-sitemonitoring and characteristic analysis o UHV transmissiontower, International Journal o Distributed Sensor Networks, vol.

, Article ID , pages, .[] E. Simiu and R. Scanlan,Wind Effects on Structures, John Wiley

and Sons, New York, NY, USA, rd edition, .

[] M. K. S. Madugula, Dynamic Response o Lattice owers andGuyed Masts, AmericanSociety oCivilEngineers(ASCE), NewYork, NY, USA, .

[] IEC, Design Criteria o Overhead ransmission Lines. Inter-national Standard IEC-, International ElectrotechnicalCommission (IEC), Geneva, Switzerland, .

[] E. Savory, G. A. R. Parke, M. Zeinoddini, N. oy, and P.Disney, Modelling o tornado and microburst-induced windloading and ailure o a lattice transmission tower,EngineeringStructures, vol. , no. , pp. , .


18/21


19/21


[] . . Fujita, Te Downburst, Report o Projects NIMROD andJAWS, University o Chicago, .

[] J. D. Holmes, A review o the design o transmission linestructures or wind loads, CSIRO Research Report -(M),Canberra, Australia, .

[] M. Ivan, Ring-vortex downburst model or ight simulations,

Journal o Aircraf, vol. , no. , pp. , .[] D. D. Vicroy, Assessment o microburst models or downdrafestimation,Journal o Aircraf, vol. , no. , pp. ,.

[] A. Y. Shehata, A. A. El Damatty, and E. Savory, Finite elementmodeling o transmission line under downburst wind loading,Finite Elements in Analysis and Design, vol. , no. , pp. ,.

[] A. Y. Shehata and A. A. El Damatty, Behaviour o guyedtransmission line structures under downburst wind loading,Wind and Structures, An International Journal, vol. , no. , pp., .

[] A. Y. Shehata and A. A. El Damatty, Failure analysis o atransmission tower during a microburst,Wind and Structures,

An International Journal, vol. , no. , pp. , .[] M. M. Darwish, A. A. E. I. Damatty, and H. Hangan, Dynamic

characteristics o transmission line conductors and behaviourunder turbulent downburst loading,Wind and Structures, AnInternational Journal, vol. , no. , pp. , .

[] M. M. Darwish and A. A. El Damatty, Behavior o selsupported transmission line towers under stationary downburstloading,Wind and Structures, An International Journal, vol. ,no. , pp. , .

[] E. omokiyo, J. Maeda, N. Ishida, and Y. Imamura, yphoondamage analysis o transmission towers in mountainous regionso Kyushu, Japan,Wind and Structures, An International Jour-nal, vol. , no. , pp. , .

[] M. F. Huang, W. Lou, L. Yang, B. Sun, G. Shen, and K. .se, Experimental and computational simulation or windeffects on the Zhoushan transmission towers, Structure andInrastructure Engineering, vol. , no. , pp. , .

[] H. Z. Deng, Q. Jiang, F. Li, and Y. Wu, Vortex-inducedvibration tests o circular cylinders connected with typicaljoints in transmission towers,Journal o Wind Engineering andIndustrial Aerodynamics, vol. , no. , pp. , .

[] H. Deng, R. Si, X. Hu, and C. Duan, Wind tunnel studyon wind-induced vibration responses o a UHV transmissiontower-line system,Advances in Structural Engineering, vol. ,no. , pp. , .

[] H. N. Li, S. Y. ang, and . H. Yi, Wind-rain-induced vibrationtest and analytical method o high-voltage transmission tower,

Structural Engineering and Mechanics, vol. , no. , pp. , .

[] E. Savory, G. A. R. Parke, P. Disney, N. oy, and M. Zein-oddini, Field measurements o wind-induced transmissiontower oundation loads,Wind and Structures, An InternationalJournal, vol. , no. , pp. , .

[] E. Savory, G. A. R. Parke, P. Disney, and N. oy, Wind-induced transmission tower oundation loads: a eld study-design code comparison, Journal o Wind Engineering andIndustrial Aerodynamics, vol. , no. -, pp. , .

[] C. B. Gurung, H. Yamaguchi, and . Yukino, Identicationo large amplitude wind-induced vibration o ice-accretedtransmission lines based on eld observed data, EngineeringStructures, vol. , no. , pp. , .

[] H. Yamaguchi, C. B. Gurung, and . Yukino, Characterizationo wind-induced vibrations in transmission lines by single-channel eld data analysis, Wind and Structures, An Interna-tional Journal, vol. , no. , pp. , .

[] M. akeuchi, J. Maeda, and N. Ishida, Aerodynamic dampingproperties o two transmission towers estimated by combiningseveral identication methods, Journal o Wind Engineeringand Industrial Aerodynamics, vol. , no. , pp. , .

[] H.-N. Li, W.-L. Shi, G.-X. Wang, and L.-G. Jia, Simpliedmodels and experimental verication or coupled transmissiontower-line system to seismic excitations,Journal o Sound andVibration, vol. , no. , pp. , .

[] K. aniwaki and S. Ohkubo, Optimal synthesis method ortransmission tower truss structures subjected to static andseismic loads, Structural and Multidisciplinary Optimization,vol. , no. , pp. , .

[] Y.H. Lei and Y. L. Chien, Seismic analysis o transmissiontow-ers under various line congurations, Structural Engineeringand Mechanics, vol. , no. , pp. , .

[] W. M. Wang, H. N. Li,and L. ian, Progressivecollapse analysis

o transmission tower-line system under earthquake,AdvancedSteel Construction, vol. , no. , pp. , .

[] L. ian, H. Li, and G. Liu, Seismic response o powertransmission tower-line system subjected to spatially varyingground motions,Mathematical Problems in Engineering, vol., Article ID , pages, .

[] H.-N. Li, F.-L. Bai, L. ian, and H. Hao, Response o atransmission tower-line system at a canyon site to spatiallyvarying ground motions,Journalo Zhejiang University: ScienceA, vol. , no. , pp. , .

[] . Li, L. Hongnan, and L. Guohuan, Seismic response o powertransmission tower-line system under multi-component multi-support excitations,Journal o Earthquake and sunami, vol. ,

no. , Article ID , .[] F.-L. Bai, H. Hao, K.-M. Bi, and H.-N. Li, Seismic response

analysis o transmission tower-line system on a heterogeneoussite to multi-component spatial ground motions,Advances inStructural Engineering, vol. , no. , pp. , .

[] B. Chen, Z. W. Chen, Y. Z. Sun, and S. L. Zhao, Conditionassessment on thermal effects o a suspension bridge basedon SHM oriented model and data,Mathematical Problems inEngineering, vol. , Article ID , pages, .

[] Y. Xia, B.Chen, X.-Q.Zhou, and Y.-L.Xu,Field monitoring andnumerical analysis o sing Ma suspension bridge temperaturebehavior, Structural Control and Health Monitoring, vol. , no., pp. , .

[] B. Chen, Y. Z. Sun, G. J. Wang, and L. Y. Duan, Assessment ontime-varying thermal loading o engineering structures basedon a new solar radiation model, Mathematical Problems inEngineering, vol. , Article ID , pages, .

[] V. . Morgan and D. A. Swif, Jump height o overhead-line conductors afer the sudden release o ice loads, TeProceedings o the Institution o Electrical Engineers, vol. , no., pp. , .

[] Y. Matsubayashi, Teoretical considerations o the twistingphenomenon o the bundle conductor type transmission line,Sumitomo Electric echnical Review, vol. , pp. , .

[] O. Nigol, G. J. Clarke, and D. G. Havard, orsional stability obundle conductors, IEEE ransactions on Power Apparatus andSystems, vol. , no. , pp. , .


20/21


[] D. G. Havard and P. V. Dyke, Effects o ice on the dynamicso overhead lines. Part II: eld data on conductor galloping,ice shedding and bundle rolling, in Proceeding o the thInternational Workshop Atmospheric Icing Structures, pp. , Montreal, Canada, .

[] A. Jamaleddine, G. McClure, J. Rousselet, and R. Beauchemin,Simulation o ice-shedding on electrical transmission lines

using adina, Computers and Structures, vol. , no. -, pp. , .

[] M. Roshan Fekr and G. McClure, Numerical modelling o thedynamic response o ice-shedding on electrical transmissionlines,Atmospheric Research, vol. , no. -, pp. , .

[] G. McClure and M. Lapointe, Modeling the structural dynamicresponse o overhead transmission lines,Computers and Struc-tures, vol. , no. , pp. , .

[] J. Jakse, M. . Al Harash, and G. McClure, Numerical mod-elling o snow-shedding effects on a kV overhead power linein Slovenia, in Proceedings o the th International Offshore andPolar Engineering Conerence, pp. , Stavanger, Norway,June .

[] . Kalman, M. Farzaneh, and G. McClure, Numerical analysiso the dynamic effects o shock-load-induced ice shedding onoverhead ground wires,Computers and Structures, vol. , no.-, pp. , .

[] L. E. Kollar and M. Farzaneh, Vibration o bundled conductorsollowing ice shedding,IEEE ransactions on Power Delivery,vol. , no. , pp. , .

[] L. E. Kollar and M. Farzaneh, Modeling the dynamic effectso ice shedding on spacer dampers,Cold Regions Science andechnology, vol. , no. -, pp. , .

[] Y. Fengli, Y. Jingbo, H. Junke, and F. Dongjie, Numericalsimulation on the HV transmission tower-line systemunder iceshedding, inProceedings o the ransmission and DistributionConerence and Exposition: Asia and Pacic, and D Asia, pp.

, Seoul, Republic o Korea, October .[] Y. Fengli, Y. Jingbo, H. Junke, and F. D. Jie, Dynamic responseso transmission tower-line system under ice shedding, Interna-tional Journal o Structural Stability and Dynamics, vol. , no., pp. , .

[] F. Yang, J. Yang, and Z. Zhang, Unbalanced tension analysisorUHV transmission towers in heavy icing areas, Cold RegionsScience and echnology, vol. , pp. , .

[] Q. Xie and L. Sun, Failure mechanism and retrotting strategyo transmission tower structures under ice load, Journal oConstructional Steel Research, vol. , pp. , .

[] L. E. Kollar and M. Farzaneh, Modeling sudden ice sheddingrom conductor bundles, IEEE ransactions on Power Delivery,vol. , no. , pp. , .

[] F. L. Yang, J. B. Yang, Z. F. Zhang, H. J. Zhang, and H. J. Xing,Analysis on the Dynamic responses o a prototype line romiced broken conductors,Engineering Failure Analysis, vol. ,pp. , .

[] B. Chen, J. Zheng, and W. L. Qu, Wind-induced vibration con-trol o transmission tower using magnetorheological dampers,in Proceedings o International Conerence on Health Monitoringo Structure, Materials and Environment, vol. -, pp. ,Nanjing, China, .

[] B. Chen, J. Zheng, and W. L. Qu, Vibration control anddamage detection o transmission tower-line system underearthquake by using riction dampers, in Proceedings o the thInternational Symposium on Structural Engineering, pp. , Guangzhou, China, .

[] Y. L. Xu and B. Chen, Integrated vibration control and healthmonitoring o building structures using semi-active rictiondampers: part I-methodology,Engineering Structures, vol. ,no. , pp. , .

[] B. Chen and Y. L. Xu, Integrated vibration control and healthmonitoring o building structures using semi-active rictiondampers: part IInumerical investigation,Engineering Struc-tures, vol. , no. , pp. , .

[] B. Chen, J. Zheng, and W. L. Qu, Practical method or wind-resistant design o transmission tower-line system by usingviscoelastic dampers, inProceedings o the nd InternationalConerence on Structural Condition Assessment, Monitoring andImprovement, pp. , Changsha, China, .

[] L. ian, Q. Q. Yu, and R. S. Ma, Study on seismic controlo power transmission tower-line coupled system under multi-component excitations,Mathematical Problems in Engineering,vol. , Article ID , pages, .

[] P. Zhang, G. B. Song, H. N. Li, and Y. X. Lin, Seismic controlo power transmission tower using pounding MD, Journal oEngineering Mechanics, vol. , no. , pp. , .


21/21

Submit your manuscripts at

http://www.hindawi.com

Documents

Dynamic Responses and Vibration Control of the Transmission