The Mechanical Properties of a Novel STMR Damper Based on Magnetorheological Silly …downloads.hindawi.com/journals/amse/2018/2681461.pdf · 2019-07-30 · ResearchArticle The Mechanical

Research ArticleThe Mechanical Properties of a Novel STMR Damper Based onMagnetorheological Silly Putty

Xiao-Guo Lin12 Fei Guo3 Cheng-Bin Du 1 and Guo-Jun Yu4

1Department of Engineering Mechanics Hohai University Nanjing 211100 China2School of Civil and Transportation Engineering Ningbo University of Technology Ningbo 315211 China3MCC Huatian Engineering amp Technology Corporation Nanjing 210019 China4Faculty of Civil Engineering and Mechanics Jiangsu University Zhenjiang 212013 China

Correspondence should be addressed to Cheng-Bin Du cbduhhueducn

Received 6 February 2018 Accepted 10 April 2018 Published 25 June 2018

Academic Editor Kestutys Baltakys

Copyright copy 2018 Xiao-Guo Lin et al +is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

A novel shear thickening magnetorheological (STMR) damper with both speed locking and semiactive controlling properties wasdesigned and fabricated based on multifunctional smart composite materials which was defined as magnetorheological Silly Putty(MRSP)+e rate sensitive property and magnetorheological effect of MRSP samples were analyzed by using a rheometer to selectthe best filler for the STMR damper +e mechanical properties of the STMR damper were investigated through slow fast anddynamic experiments +e experimental results indicate that the STMR damper exhibits an obvious rate sensitive characteristicand semiactive control property On one hand when the STMR damper is simulated fast enough it can realize the ldquospeed switchrdquofunction which enables it to instantly lock up and act as a shock transmission unit (STU) On the other hand when the STMRdamper is applied with current the damping force can be adjusted by magnetic field strength to realize its semiactive controllingproperty In addition a multiparameter and symmetry model was established to describe the dynamic hysteretic behavior of theSTMR damper which is consistent with the experimental data

1 Introduction

Magnetorheological Silly Putty (MRSP) is a smart multi-functional composite prepared by dispersing soft magneticparticles into a Silly Putty matrix with shear stiffeningproperty [1] +is new kind of smart material is the solid stateof the magnetorheological shear thickening fluid (MRSTF)proposed by Zhang et al and Peng et al [2 3] SubsequentlyWang et al [4 5] first developed a magnetically responsiveshear-stiffening gel with excellent shear stiffening perfor-mance andmagnetorheological effect+is novelmagneticallyresponsive shear-stiffening gel can provide credible tunabilitywith external stimuli

At this stage the vibration damper based on a singlemagnetorheological material requires an external magneticfield which belongs to the active device Magnetorheologicalmaterials are widely used in all kinds of MR dampers and thetechnology is relatively mature Lord Company of USA and

BASF Company of Germany have developed many com-mercialized MR dampers For example the RD-1005-type MRdamper produced by Lord Company is the earliest applicationof the international commercializedMR damper with dampingforce over 2200N [6] MR dampers designed for large civilengineering structures show greater structure size and dampingforce output Qu et al developed a full-scale MR damperoutput of up to 500 kN carried out a study on the key tech-nologies of the leakproof design of themagnetic field and built-in butterfly spring and finally applied the full size MR damperto a highway railway cable-stayed bridge with semiactive vi-bration control [7ndash10] Yu et al developed the self-decoupledmagnetorheological (SDMR) damper which produced thelargest output of 360 kN +e displacement decouplingmechanism was set up in the damper and permanent magnetswere arranged to provide the function of self-protection +eSDMR damper was mainly applied to the semiactive vibrationcontrol of frame and grid structures [11ndash14]

HindawiAdvances in Materials Science and EngineeringVolume 2018 Article ID 2681461 15 pageshttpsdoiorg10115520182681461

+e single shear thickening material is used as energydissipation fillers for small passive ST dampers Zhang et aldeveloped a speed-driven damper based on the shearthickening fluid and studied the dynamic performance of theST damper through both experiment and theory methods[15]+ese results confirm that the STdamper presents higherstiffness and damping at high-speed dynamic loading thanthose at low-speed loading and absorbs more energy Zhouet al developed a double-out rod-type ST damper filled byshear thickening fluid of a high-concentration polystyrene-ethyl acrylate nanometer particle suspension +e dynamicalexperiment results reveal that with the increase in excitationfrequency the storage modulus and energy dissipationmodulus rapidly increase and the output of the ST damperdramatically boosts exhibiting great absorption and energydissipation capacity the maximum energy dissipationmodulus reached up to 21 kPa [16] +e most common ap-plication of shear thickening materials in civil engineeringstructures is the shock transmission unit (STU) which isa device resembling a speed switch It is basically approxi-mating to a general damper in appearance and internalstructure which is composed of a piston and cylinder andregarded as a special damper Silly Putty has becomea promising material for the special damper of STU which iswidely used in the multispan bridge [17]

+e MR damper is the most mature energy dissipationdevice in the field of magnetorheological vibration dampingFrom the point of energy the principle of the work is tochange the energy spectrum of the vibration sourcersquos ex-citation to the system and reduce the passed energy tosuppress the vibration However in the face of huge in-centive loads the vibration damping which the MR damperdepends on does not slow down the deformation or evendestruction of civil engineering structures due to insufficientstiffness besides the mechanism of damping is relativelysimple In addition these MR dampers all belong to activedevices whichmeans that in the event of a circuit failure thatcannot be controlled by a magnetic field the damper losesthe significance of the semiactive vibration control +ecurrent solutions include setting a permanent magnet tomake the magnetorheological fluid in the MR damperproduce certain yield strength but the scheme makes thedesign of the damper more complex Furthermore com-monly used permanent magnets are made of NdFeBmaterialwith strong temperature instability meaning that the higherthe temperature the faster the demagnetization +e shearthickening material is mainly used in caging devices in-cluding all kinds of speed locking devices in order to im-prove the overall stiffness of the structure and achieve thepurpose of seismic resistance and vibration reduction At themoment researchers of the world only focus on the study ofthe mechanisms of magnetorheological damping and shearthickening damping respectively and there is no in-tersection between each other However there are no rel-evant studies that combine the characteristics of two kinds ofintelligent materials as a whole to explore new intelligentdampers with double vibration damping mechanisms

In this work a novel shear thickening magneto-rheological (STMR) damper was designed and fabricated

based onMRSPs Compared with traditionalMR dampers theSTMR damper not only exhibited controllable characteristicsof damping force under the adjustment of the magnetic fieldbut also provided a ldquolockingrdquo function under an unexpectedsudden rare load which was more suitable for the vibrationcontrol of large civil engineering structures In order to verifythe dual vibration damping characteristics of the STMRdamper slow fast and dynamic mechanical property ex-periments were carried out Finally a multiparameter andsymmetry model was established and deduced to describe thedynamic hysteretic behavior of the STMR damper

2 Experimental Section of MRSPs

21 Materials +e Dow Corning 3179 dilatant compoundwhich was purchased from Dow Corning Co Ltd was usedas the Silly Putty matrix +e composition of the Silly Puttymatrix is outlined in Table 1 Polydimethylsiloxane (PDMS)as a commonly used organic silicon material is the majorconstituent of the composition +e soft magnetic particles ofthe carbonyl iron (CI) with an average size of 35 μm werepurchased from Jiangsu Tianyi Ultra-fine metal powder CoLtd (Xuyi China)

22 Preparation and Testing of MRSPs +e dilatant com-pound as matrix and the different volume fractions of CI asfillers were homogeneously mixed using a two-roll mill(Nantong Hailite Rubber Machinery Inc China XK-160model) at room temperature For the mechanical mixingmethod up to six different volume fractions were consideredfor the present study 0 698 1011 1584 2080 and 2729+e prepared samples were marked as MRSP 0 MRSP 1MRSP 2 MRSP 3 MRSP 4 and MRSP 5 in sequence In thiswork the dynamic rheological properties of theMRSP sampleswere carried out using a commercial rheometer (Physica MCR302 Anton Paar Co Austria) During the testing procedurea parallel plate PP20 with a diameter of approximately 20mmwas used and a gap of 1mmwasmaintained at all times At thesame time a controllable magnetic field was generated by anexternal coil Besides all the samples for the experiment weremaintained at an approximately same volume value+eMRSPsample and MCR 302 rheometer are displayed in Figure 1

3 Experimental Section of the STMR Damper

31 Designing of STMRDamper +e structure of the STMRdamper is shown in Figure 2 with its appearance

Table 1 Composition of the Silly Putty matrix

Composition Weight percentagePolydimethylsiloxane (PDMS) 65Silica 17+ixotrol 9Boric acid 4Glycerine 1Titanium dioxide 1Dimethyl cyclosiloxane 1

2 Advances in Materials Science and Engineering

approximating to a traditional MR damper mainly con-sisting of the main cylinder tube accessory cylinder tubeauxiliary cylinder main piston accessory piston and pistonrod +e filling material in the main cylinder exhibits high-MR effect while the inner filling material of the auxiliarycylinder presents a higher shear stiffening effect to improvethe overall safety reserve So both the main cylinder andauxiliary cylinder are combined together into a cooperativecylinder +e main piston and auxiliary piston are arrangedon the piston rod the main piston and piston rod areconnected with the method of a rigid threaded connectionand two circular excitation coils are detoured in two op-posite directions on the main piston Each of the two ex-citation coils connects one wire to the external power supplythrough the traverse channel and the power mode is in theparalleling way +e accessory piston is connected with thepiston rod through the butterfly spring and allows it to movealong the piston rod within the maximum compressionamount of the spring in order to realize the decouplingfunction +e filling materials in the main and auxiliarycylinders generate flow and deformation in their ownworking gaps

+e STMR damper mainly consists of the main cylindercontrolled by magnetorheology and the accessory cylinderwith displacement decoupling characteristic +is noveldamper not only maintains the performance of an adjustabledamping force by magnetic field but also possesses obviousrate sensitive characteristic which provides the function oflocking structure to disperse loading under high frequencyor impaction +e basic structural parameters of the STMRdamper are listed in Table 2

32 Testing of the STMRDamper +e physical object of theSTMR damper is displayed in Figure 3 +e energy dissi-pation of the STMR damper is mainly triggered by the flowand deformation of the filling materials +e rate sensitive

characteristic and magnetorheological effect of MRSPs arethe internal reasons for the damper to adapt to environ-mental incentives and directional intelligent controllabil-ity In order to verify the rate sensitivity and magneticcontrol characteristics of the STMR damper the me-chanical properties were investigated by the SDS-300electrohydraulic servostatic and dynamic testing ma-chine +e main contents of the testing included the fol-lowing (1) the influence of different rates on themechanical properties of the damper under slow and fastaxial tension conditions (2) the influence of differentfrequencies and different current excitations on the dy-namic hysteretic properties of the damper under large andsmall displacements+e installation of the testing machinefor the STMR damper is displayed in Figure 4 In the testingprocedure a current excitation with an adjustable DC-regulated power supply was adopted and the maximuminput current was 3 A In each experiment the pistoncarried on the reciprocating movement from the balanceposition which was mainly located in the middle positionbetween the main and accessory cylinder tubes In thedamper structure diagram the limit stroke of the pistonwas 65mm and in the present experiment of dynamicmechanical properties the amplitude of the large dis-placement was 55mm

4 Results and Discussion

41 Rate Sensitive Characteristic of MRSPs In the earlierresearch when there was no external magnetic field appliedthe soft magnetic particles of CI were evenly dispersed in theSilly Putty matrix to form isotropic viscoelastic materials[1] From this point the CI powder was considered asa general particle filling which played a role in strength-ening the matrix material +e larger the volume fraction ofthe CI particle is the greater the shear storage modulus ofthe sample becomes which is in consistent with the

(a) (b)

Figure 1 Preparation of (a) the MRSP sample and (b) the MCR 302 rheometer

Advances in Materials Science and Engineering 3

empirical formula (1) is formula explains the rule ofshear modulus varying with the volume fraction of rigidparticles randomly lled in the rubber matrix [18] eaddition of rigid particles leads to the decrease in internalmotion space within the matrix which further promotes theinteraction between the molecular chains Simultaneouslymore obvious obstacles are encountered in solving the

entanglement of the molecular chains which shows theescalation in shear storage modulus on a macroscopic pointof view [5]

Gran G0 1 + 25ϕ + 141ϕ2( ) (1)

where Gran refers to the shear modulus of composites lledwith rigid particle compositesG0 is the shear modulus of the

32

33

31

30

29

28

27

26

25

24

23

22

21

20

19

18

17

16

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

Assembly drawing of STMR damper

SerialNumber Name Quantity

2Filling materials33

4Hexagon head bolt32

2Seal ring of type Yx31

1Front end cover30

8Screw29

1Main piston 328

1Main cylinder tube27

1Coil26

4Seal ring of type O25

2Magnetically isolatedcopper piece24



1Semiring sleeve21

2Semiring20

2Sleeve baffle19


1Accessory cylinder tube17

4Pull rod bolt 216

1Back end cover15

1Auxiliary cylinder tube14

1Connecting cylinder cover 213

1Accessory piston 212

4Butterfly spring11

1Accessory piston sleeve10



1Main piston 27

1Coil sleeve6

1Main piston 15


4Pull rod bolt 13

1Piston rod2

1Single earring for axial use1

Figure 2 Basic structure of the STMR damper


matrix material without the filling of rigid particles and ϕmeans the volume fraction of rigid particles

Besides from the earlier research in order to comparethe shear stiffening degree of theMRSP samples the absoluteshear stiffening effect (ASTe) and relative shear stiffeningeffect (RSTe) are defined as the index of measurement [1] asshown specifically in the following formula

ASTe Gprimemax minusGprimemin

RSTe Gprimemax minusGprimemin

Gprimemintimes 100

(2)

where Gprimemax stands for the maximum shear storage modulusexcited by the loading frequency and Gprimemin refers to the initial

shear storage modulus When the angular frequency in-creases the MRSP samples exhibit an obvious rate sensitivecharacteristic and a sharply increased storage modulustogether with the demonstration that the sample ldquohardensrdquoFurthermore the higher the content of the CI powder is themore beneficial it is to the absolute shear stiffening effect ofthe material In earlier research [1] for the MRSP 5 sampleunder normal temperatures the absolute modulus change is06145MPa which equals to approximately twice the pureshear stiffening matrix MRSP 0 while the relative shearstiffening effect is 141264 which is far less than 7758421of the pure shear stiffening matrix MRSP 0

However under the condition of an external magneticfield the soft magnetic particles of the CI powder werearranged into chain-like ordered structures along the directionof the magnetic flux line in the interior of the shear stiffeningmatrix forming the anisotropic structure +e pure shearstiffening matrix MRSP 0 sample was not influenced by themagnetic field due to the absence of soft magnetic particlefillings Figure 5 illustrates the relationship between shearstorage modulus of the MRSP samples with different contentsof soft magnetic particles and the angular frequencies sepa-rately under different external magnetic fields in which theangular frequency is 1ndash100 rads with continuous change It isobserved from the diagram that with the strength of theexertedmagnetic field enhancing the shear storagemodulus ofthe sample increases as well For the MRSP 5 sample themaximum storage modulus after shear stiffening is approx-imately 05MPa under the condition of zero magnetic fieldNonetheless under the constant magnetic flux density of0627T the maximum storage modulus after shear stiffeningis up to 23MPa and the magneto-induced modulus causedby the magnetic field equals to approximately 18MPa Forthe transverse comparison between different samples whenthe content of the CI powder rises up the storage modulus atthe same magnetic flux density keeps an upward tendency+e maximum storage modulus of the MRSP 1 sample undera magnetic flux density of 0627T is 06MPa while theparticle mass fraction of MRSP 5 reaches twice as much asthat of MRSP 1 but the maximum modulus equals toapproximately four times as that of MRSP 1 On one hand nomatter how the soft magnetic particles are randomly filled orarranged in the matrix with a certain ordered structure underthe situation that the content of soft magnetic particles growsup the reinforcement effect of the material increases On theother hand previous studies expose that the higher the

Table 2 Main structure parameter of the STMR damperWorking gap of the main cylinder tube 2mm Working gap of the accessory cylinder 2mmExternal diameter of the main piston 156mm External diameter of the accessory piston 156mm

Wall thickness of steel tube of the main cylinder tube 15mm Wall thickness of steel tube of the accessory cylindertube 15mm

Pistonrsquos stroke limit of the main cylinder tube 65mm Pistonrsquos stroke limit of the accessory cylinder tube 65mmLength of working gap of the main cylinder tube 206mm Length of working gap of the accessory cylinder tube 117mmPistonrsquos number of windings of the main cylindertube 980 Effective stroke of decoupling spring 7mm

Diameter of piston rod 50mm Maximum power lt120WPistonrsquos current range of the main cylinder tube 0sim3A Designed damping force 300 kN

Figure 3 Entity of the STMR damper

Figure 4 +e experimental setup of the STMR damper


06

05

04

03

02

01

00

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)

0 20 40 60 80 100Angular frequency ω (rads)

0 T0102 T0211 T

0321 T0430 T

0533 T0627 T

(a)

12

10

08

06

04

02

00

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


0 T0102 T0211 T

0321 T0430 T

0533 T0627 T

(b)

0 20 40 60 80 100

14

16

18

12

10

08

04

02

00

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)

Angular frequency ω (rads)

0 T0102 T0211 T

0321 T0430 T

0533 T0627 T

(c)

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


2624222018161412100806040200

0 T0102 T0211 T

0321 T0430 T

0533 T0627 T

(d)

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


2624222018161412100806040200

0 T0102 T0211 T

0321 T0430 T

0533 T0627 T

(e)

Figure 5 e shear storage modulus of MRSP samples as a function of angular frequency at dierent magnetic ux densities (a) MRSP 1(b) MRSP 2 (c) MRSP 3 (d) MRSP 4 and (e) MRSP 5


volume fraction of particles the denser the chain-like orderedstructures form under the same magnetic field conditionwhich leads to the increasing of themagneto-inducedmodulus

Similarly the ASTe and RSTe indexes are implementedto illustrate the influence of magnetic flux density on theshear stiffening effect of the MRSP samples and the rel-evant parameters are listed in Table 3 It is perceived thatfor samples with low content of soft magnetic particlessuch as MRSP 1 and MRSP 2 the magnetic flux density isconducive to the promotion of the shear stiffening effect ofthe MRSP samples +e greater the magnetic flux density isthe more superior the value of the ASTe becomes Forsamples with volume fraction of soft magnetic particle upto 15 such as MRSP 3 MRSP 4 and MRSP 5 the in-fluence of magnetic flux density on absolute shear stiffeningeffect is relatively complex With the increase of magneticflux density ASTe presents a tendency of falling down afterascending first which demonstrates that only under weakmagnetic field conditions (no more than 01 T) it becomesconducive to the absolute shear stiffening effect of highparticle content samples Besides with the increase of

magnetic flux density the initial shear storage modulus ofthe samples significantly intensifies while the relative shearstiffening effect of samples declines and the RSTe valuedecreases However for the transverse comparison betweendifferent samples under the zero magnetic field conditionsthe higher the particle content of the sample becomes thegreater the absolute shear stiffening effect it achieves whichis in line with the previous description As the intensity ofthe magnetic field increases for the samples with the higherparticle content the ASTe value becomes smaller Whenthe magnetic flux density is 0627 T the change in theabsolute modulus of MRSP 2 is 0729MPa Neverthelesswith the increase of particle content the ASTe value of thesample subsequently declines and in addition the absolutemodulus of MRSP 5 drops to only 022MPa Under zeromagnetic field condition the filling of soft magnetic par-ticles plays a certain positive role in the absolute moduluschange in the MRSP samples As the magnetic flux densityincreases the ordered structure of the soft magnetic par-ticles in the interior of the matrix becomes more complex+e larger the volume fraction is the closer the connections

Table 3 Gprimemax Gprimemin ASTe and RSTe of the MRSP samples

Samples Magnetic flux density B (T) Gprimemax (MPa) Gprimemin (MPa) ASTe (MPa) RSTe ()

MRSP 1

0 0287 000346 028354 8194800102 0349 001620 033280 2054320211 0480 006410 041590 648830321 0566 010900 045700 419270430 0603 013400 046900 3500533 0618 014400 047400 329170627 0627 015000 047700 318

MRSP 2

0 0309 000531 030369 5719210102 0383 003550 034750 978870211 0873 022900 064400 281220321 1060 037000 069000 186490430 1160 044000 072000 163640533 1190 045900 073100 159260627 1200 047100 072900 15478

MRSP 3

0 0411 00131 039790 3037400102 0924 02900 063400 218620211 1280 06690 061100 91330321 1500 09190 058100 63220430 1610 10400 057000 54810533 1670 10900 058000 53210627 1710 11300 058000 5133

MRSP 4

0 044 00228 041720 1829820102 124 0366 087400 238800211 190 119 071 59660321 214 159 055 34590430 224 177 047 26550533 231 186 045 24190627 231 192 039 2031

MRSP 5

0 051 00239 04861 2033890102 167 0814 08560 105160211 215 167 048 28740321 229 195 034 17440430 232 204 028 13730533 233 208 025 12020627 234 212 022 1038


become between particles and particles and between chainand chain thereby providing partial support for themacroscopic shear modulus However the movement ofthe matrix molecular chains is greatly hindered due to thedecrease of internal motion space within the matrix Fromthe viscoelastic aspect it is not beneficial to the relaxationand rebalance process of the high molecular polymerwhich leads to the reduction of the absolute shear stiffeningeffect of the samples +erefore for the MRSP samples witha high content of soft magnetic particles in order to givefull play to the characteristic of shear stiffening the externalmagnetic field in its working environment should not betoo large

42 Magnetorheological Effect of MRSPs Under a continu-ously changing magnetic field the soft magnetic particles arerapidly magnetized into dipoles and are arranged into chain-like ordered structures within the interior of the matrix untilthe magnetic saturation is achieved Macroscopically thecontinuous variation of the shear modulus of the MRSPseventually reaches a steady state of saturation +e mag-netorheological effect determines the directional controlla-ble performance of theMRSPs which is usually measured bythe change of modulus Currently the research results in-dicated that the lower the loading frequency was the higherthe magnetorheological effect became and the more theconducive it was to the adjustment of the magnetic fieldHowever the loading frequency was higher the matrixmodulus of MRSP became larger the chain-like resistance ofsoft magnetic particles in the interior of the matrix becamegreater and the magnetorheological effect tended to belower [1] Figure 6 reveals the varied relationship betweenthe shear storage modulus and magnetic flux density ofdifferent samples under the conditions of different shearstrain low load frequency (ω1 rads) and magnetic fluxdensity continuous changing from 0 to 0894 T Corre-spondingly the larger the shear strain is the smaller thestorage modulus of the sample becomes As the magneticflux density enhances the shear storage modulus rapidlyincreases before 04 T and gradually tends to magneticsaturation after 04 T Likewise the absolute magneto-rheological effect (AMRe) and relative magnetorheologicaleffect (RMRe) are adopted as the indexes for the perfor-mance of magnetic field adjustment as shown in the fol-lowing equation

AMRe Gprimemax minusGprimemin

RMRe Gprimemax minusGprimemin

Gprimemintimes 100

(3)

where Gprimemax means the maximum shear storage moduluswhen reaching magnetic saturation while Gprimemin is the initialshear storage modulus under zero magnetic field +ecorrelated results of all the curves in Figure 6 which arecalculated according to (3) are listed in Table 4

For the transverse comparison of the samples withdifferent contents of soft magnetic particles the larger the

volume fraction of soft magnetic particles is the greater themagneto-induced modulus becomes and the more obviousthe absolute magnetorheological effect tends to be ForMRSP 5 with the highest particle content the magneto-induced modulus is up to 15MPa at the strain of 05 +erelative magnetorheological effect is mainly determined bythe initial shear storage modulus from which it can beobserved that for loading conditions at small strains of05 and 1 the relative magnetorheological effect pro-duced by the same sample varies with no obvious differencefrom each other +is is for the reason that within the strainof 1 each group of MRSP sample is in the linear vis-coelastic region which displays no obvious difference ofinitial modulus However when the strain continues toclimb up to 5 and 10 respectively the initial modulussharply decreases outside the linear viscoelastic region andin turn the magnetorheological effect becomes quite dif-ferent Besides the relative magnetorheological effect withstrain of 10 is higher than that with the strain of 5 Withthe increase in the content of CI powder the relativemagnetorheological effect tends to enhance When thestrain is 05 the relative magnetorheological effect ofMRSP 5 reaches 352 at most nevertheless if the shearstrain increases to 10 the relative magnetorheologicaleffect of MRSP 4 reaches as high as 617 and the adjustablerange of the magnetic field is relatively wide Consequentlyit is beneficial to obtain great magnetorheological effectwhen the volume fraction of the soft magnetic particle ishigh

43 Slow and Fast Mechanical Properties of the STMRDamper By comparing the rate sensitive characteristic andmagnetorheological effect of each MRSP samples the MRSP5 sample with high magnetorheological effect was finallyselected as the filling material in the main cylinder tube ofthe STMR damper Since there was no soft magnetic par-ticles filled in MRSP 0 sample due to its higher relative shearstiffening effect it was regarded as the fillingmaterials for theaccessory cylinder tube of the STMR damper For the STMRdamper with the locking function when the relative speedrate of the piston to the cylinder is slower than 1mms it isconsidered as a slow testing but when the speed rate is greaterthan 1mms it is regarded as a fast testing Firstly in order tomeet the requirements of the slow testing the control rateswere set constantly as 0033mms 0083mms 0166mms033mms 066mms and 083mms respectively Figure 7is the force-displacement curve of the STMR damper whenthe control rate is 0033mms from which it is clear that thewhole region is approximately divided into three parts elasticregion viscoelastic region and viscous region +e force-displacement curve displays a linear relationship in theelastic region a nonlinear relationship in the viscoelasticregion and gradually reaches stability in the viscous regionwhich tends to a certain value According to the force-displacement curve of the elastic region and Hookersquos lawthe elastic stiffness K of the STMR damper at differenttensile rates is calculated Figure 8 shows the relationshipbetween the elastic stiffness of the STMR damper and the


γ = 5γ = 10 γ = 1

γ = 05

020

018

016

014

012

010

008

006

004

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)

00 01 02 03 04 05 06 07 08 09Magnetic flux density B (T)

(a)

γ = 5γ = 10 γ = 1

γ = 05

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


036034032030028026024022020018016014012010008006004

(b)

γ = 5γ = 10 γ = 1

γ = 05

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


12

10

08

06

04

02

00

(c)

γ = 5γ = 10 γ = 1

γ = 05

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


18

16

14

12

10

08

04

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02

00

(d)

γ = 5γ = 10 γ = 1

γ = 05


Shea

r sto

rage

mod

ulus

Gprime (

MPa

) 18

20

16

14

12

10

08

04

06

02

00

(e)

Figure 6 e shear storage modulus of MRSP samples as a function of magnetic ux density at dierent shear strains (a) MRSP 1 (b)MRSP 2 (c) MRSP 3 (d) MRSP 4 and (e) MRSP 5


control rate from which it is detected that the greater thecontrol rate is the greater the elastic stiness of the STMRdamper becomes When the set control rate equals to0033mms elastic stiness tends to be less than 30 kNmmhowever when the control rate is up to 083mms theelastic stiness exceeds 65 kNmm which is twice as muchas that of the former Accordingly it proves that under thecondition of a slow testing the STMR damper exhibitsa certain rate sensitive characteristic

e fast testing displays that the STMR damper can beinstantaneously locked at a certain rate to transfer thedesigned load According to AASHTO when a fast testing iscarried out the locking distance should be within 12mm[19] Figure 9 shows the force-displacement curves with

a constant control rate of 6mms 8mms and 10mmsrespectively It is observed that when the force is loaded from0 to 300 kN the locking distances under the three controlrates are all less than 12mm which is in full compliance withthe provisions of AASHTO Nevertheless when the controlrate increases the lock distance and locking time tend toshorten e locking distance under the control rate of10mms is approximately 8mm and the locking time is only08 s which achieves instant locking while on the otherhand the lock times of the other two groups under thecontrol rates are both more than one second ereforecombined with these experimental results the developedSTMR damper accomplishes the locking function withina short time and distance which reveals that the STMRdamper can be simplied as a ldquorate switchrdquo with a lockingrate of 10mms meaning that instant locking happens whenthis rate is exceeded

44 Dynamic Mechanical Properties of the STMR DamperWhen the amplitude is within the range of the maximumcompression of the buttery spring only the main piston of

100

80

60

40

20

Forc

e (kN

)

Displacement (mm)20 22 24 26 28 30

Viscoelastic region Viscous region

Elastic region

Figure 7 Division of the displacement-resistance region

0 10 20 30 40 50

70

65

60

55

50

45

40

35

30

25

Stiff

ness

K (k

Nm

m)

Velocity v (mmmin)

066 mms

033 mms

083 mms

0166 mms

0083 mms

0033 mms

Figure 8 Relationship between velocity and spring stiness

Table 4 Gprimemax Gprimemin AMRe and RMRe of the MRSP samples

SamplesShearstrain

c

Gprimemax(MPa)

Gprimemin(MPa)

AMRe(MPa)

RMRe()

MRSP 1

05 0184 00666 01174 176281 0167 00619 01051 169795 0119 00547 00643 1175510 0100 00393 00607 15445

MRSP 2

05 0340 00796 02604 327141 0281 00692 02118 306075 0169 00590 01100 1864410 0135 00398 00952 23920

MRSP 3

05 1120 02770 08430 304331 0934 02390 06950 290795 0484 01150 03690 3208710 0340 00498 02902 58273

MRSP 4

05 1630 04020 12280 305471 1360 03530 10070 285275 0735 02010 05340 2656710 0480 00669 04131 61749

MRSP 5

05 1960 04340 15260 351611 1770 03660 14040 383615 0907 02140 06930 3238310 0592 00843 05077 60225

ndash2 0 2 4 6 8 10 12 14 16 18Displacement (mm)

300

250

200

150

100

50

0

Forc

e (kN

)Lock distance

10 mms

8 mms

6 mms

Figure 9 e relationship between displacement and resistanceforce


the STMR damper works When the amplitude exceeds themaximum compression of the buttery spring the main andaccessory pistons work together resulting in a greater outputof damping force Since the interior of the STMR damper islled by MRSPs with the rate sensitive characteristic it isnecessary to conrm the dynamic rate sensitive perfor-mance So the excitation frequency of 01Hz 05Hz 10Hz15Hz and 25Hz were respectively applied under a dis-placement of 5mm e experimental results are displayedin Figure 10 From the experimental curve it is sensed thatunder the condition of small displacement within a fre-quency range of 01Hzndash25Hz the damping force changesfrom 603 to 2695 kNe higher the excitation frequency isthe greater the shear rate of materials in the interior of thedamper comes to be the larger the damping force becomesand the more apparent the rate sensitive characteristic turnsout to be Besides the ratio between the maximum andminimum damping force is 45 showing that when theexcitation frequency is more than 15Hz the damping forcegradually tends to saturation and the change range islimited which is consistent with the rate sensitive perfor-mance of the MRSP samples When the excitation frequencyenhances the envelope area of the damping force-displacementcurve inclines to enlarge indicating that the energy dissipationcapacity of the STMR damper becomes stronger and thefrequency directly aects the energy dissipation capacity of theSTMR damper e force of the buttery spring is super-imposed on the STMR damper which leads to the slant of thehysteresis curve

In order to validate the adjustable characteristic of themechanical properties for the STMR damper under the eectof the magnetic eld the dynamic mechanical propertieswere investigated under dierent currents during which thesame displacement control was adopted and each workingcondition was circulated for 10 times e testing conditionswere as follows the displacement was 5mm the frequencies

were 01Hz 05Hz 10Hz and 15Hz and a current of 0 A1A 2A and 3A was applied in each case respectivelyWhen the displacement was 55mm and the frequency was01Hz a current of 0 A 1A 2A and 3A was similarlyapplied nevertheless when the input current increased insequence the magnetic ux density in the working gap of theSTMR damper also enhanced and the damping force of thedamper also correspondingly magnied as well Figure 11presents the experimental results under the above testingconditions showing from the damping force-displacementcurves that whether it is under the condition of small dis-placement or large displacement and the STMR damperexhibits certain mechanical property of magnetic eldcontrollability

As shown in Figure 11 frequency is an important factorthat aects the adjustable range of the damping force of theSTMR damper under a small displacement of 5mm InFigure 11(a) the excitation frequency is 01Hz presentingthat when the input current changes from 0 to 3A thevariation range of the damping force is 603ndash1893 kN andthe ratio between the maximum and minimum dampingforce is approximately 31 In Figures 11(b)ndash11(d) theexcitation frequencies are 05Hz 10Hz and 15Hzrespectively revealing the fact that when the current changesfrom 0 to 3A the ratio between the maximum and mini-mum damping force becomes 20 14 and 12 respectivelyAccordingly the increase of frequency directly aects theadjustable range of the damper under the excitation of themagnetic eld which demonstrates that the higher the fre-quency is the narrower the adjustable range turns out to beis is for the reason that the high excitation frequency makesthe lling materials to stien and the soft magnetic particlesin the magnetic eld are chain blocked which is not ad-vantageous to stimulate the magnetorheological eect andthereby makes the adjustable range of the damper undermagnetic eld narrow down In Figure 11(e) under thecondition of a displacement of 55mmwith low frequency andlarge displacement the damper presents the obvious char-acteristic of magnetic eld controllability When the inputcurrent changes from 0 to 3A the variation range of thedamping force is 2128ndash2721 kN and the ratio between themaximum andminimumdamping force is approximately 13When the damper is under the condition of large displace-ment since the buttery spring works together with the mainand accessory cylinder tubes after the compression limit thehysteresis curve displays a certain sag in the positive andnegative strokes

In the structural vibration control as the external ex-citation frequency is not enough to make the STMR damperinduce the speed locking it is given full play to the ad-justment ability of the damper in the magnetic eld whichindicates that the STMR damper can be simplied to a largertraditional MR damper

45 Dynamic Hysteretic Mechanical Model for the STMRDamper e dynamic damping force of the STMR dampercan be decomposed into a superposition of three compo-nents of force the rst component of force refers to applied

Displacement (mm)

300250200150100

500

ndash50ndash100ndash150ndash200ndash250ndash300

Dam

ping

forc

e (kN

)

ndash6 ndash4 ndash2 0 2 4 6

01 Hz05 Hz10 Hz

15 Hz25 Hz

Figure 10 Relationship between the damping force and dis-placement for the STMR damper


200

150

100

50

0

ndash50

ndash100

ndash150

ndash200

Dam

ping

forc

e (kN

)

ndash6 ndash4 ndash2 0 2 4 6Displacement (mm)

0 A10 A

20 A30 A

(a)

200250300

150100

500


Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(b)

200250300

150100

500


Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(c)

300

200

100

0

ndash100

ndash200

ndash300

Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(d)

300

200

100

0

ndash100

ndash200

ndash300

Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(e)

Figure 11 Relationship between damping force and displacement for the STMR damper at dierent frequencies and displacements (a)01Hz 5mm (b) 05Hz 5mm (c) 10Hz 5mm (d) 15Hz 5mm (e) 01Hz 55mm


force fmr which is produced by the magnetorheologicaleffect of the material which is related to the current orexerted magnetic field strength the second component offorce fpm stands for the applied force to describe thecharacterization of polymer properties which is connectedwith external excitation rate or strain rate as for fbs itmeans the additional force of the butterfly spring whichsatisfies with Hookersquos Law

+e first component of force fmr can be expressed as

fmr kprime1u + cprime _u + fp (4)

where kprime1 and cprime are the stiffness and damping coefficientsdepending on the magnetic field strength respectively u and_u stand for the displacement and speed rate fp is thehysteretic subitem which is controlled by the followingBoucndashWen differential equation

fprimep α _uminus β _u fp

11138681113868111386811138681113868

11138681113868111386811138681113868nminus c| _u|fp fp

11138681113868111386811138681113868

11138681113868111386811138681113868nminus1

αminus β + c sgn _ufp1113872 11138731113960 1113961 fp

11138681113868111386811138681113868

11138681113868111386811138681113868n

1113882 1113883 _u(5)

where α β c and n are all the parameters to control theshape of the hysteretic curve

+e second component of force fpm refers to the ma-terial viscoelasticity or nonlinear stiffness characteristicwhich can be expressed as

fpm kPrime1u + kPrime3u + cPrime _u (6)

where kPrime1 kPrime3 and cPrime are the stiffness and damping co-efficients depending on the speed rate or the strain raterespectively

+e third component of force fbs means the additionalforce of the butterfly spring when under the situation thatthe excitation amplitude is less than the maximum com-pression of the butterfly spring according to Hookersquos law itis expressed as

fbs kbsu (7)

where kbs stands for the stiffness of the butterfly springBased on (4) (6) and (7) the damping force of the

STMR damper can be expressed as

f fmr + fpm + fbs k1 + kbs( 1113857u + k3u3

+ c _u + λfp

(8)

where k1 kprime1 + kPrime1 k3 kPrime3 c cprime + cPrime and λ representsthe proportional coefficient between the hysteretic andnonhysteretic force All the stiffness and damping coefficientsdepend on the strain rate and magnetic field density

For the dynamic mechanical properties of the STMRdamper it can be considered that the shear storage modulusof the MRSPs contributes to the stiffness part of the devicestructure whereas the damping characteristic of the materialcontributes to the damping part of the device structureConsequently in (8) the stiffness coefficients k1 and k3damping coefficient c and ratio coefficient λ can be rewritteninto functions of magnetic field and speed rate as belowrespectively Furthermore related studies revealed that

stiffness and damping are almost linearly dependent on theexternal magnetic field and strain rate [20]

k1 k10 He( 1113857 + k11 He( 1113857| _u| + k12 He( 1113857| _u|2 (9)

k3 k30 He( 1113857 + k31 He( 1113857| _u| (10)

c c0 He( 1113857 + c1 He( 1113857| _u| (11)

λ λ0 He( 1113857 + λ1 He( 1113857| _u| (12)

where k10 k11 k12 k30 k31 c0 c1 λ0 and λ1 are ap-proximated as the linear equation of the external magneticfield He

+e displacement hysteresis phenomenon of the STMRdamper is caused by the subitem fp of the hysteretic forcetherefore in combination with (5) the hysteretic force canbe expressed as

F1 fp1113872 1113873 uminus u+

F2 fp1113872 1113873 uminus u+

F3 fp1113872 1113873 uminus uminus


or fp Fminus11 uminus u+( 1113857 _uge 0 fp ge 0

fp Fminus12 uminus u+( 1113857 _uge 0 fp le 0

fp Fminus13 uminus uminus( 1113857 _ule 0 fp ge 0

fp Fminus14 uminus uminus( 1113857 _ule 0 fp le 0

(13)

where Fi(fp) (i 1 2 3 4) represents the function of fpand Fminus1i (fp) means the inverse function of Fi(fp) Fur-thermore u+ and uminus respectively refer to the lagging dis-placement produced in the positive and negative directionsof the equilibrium position In the testing process the up-ward of the balanced position is positive while the down-ward of the balanced position is negative In a cycle once thepeak and valley values of the displacement are equal and thelagging displacement of the positive and negative directionsreaches equivalence the hysteresis curve presents thesymmetric characteristic Besides when n 1 and β c (5)can be simplified to

fp

αβ + c

1minus eminus(β+c) uminusu+( )1113876 1113877 _uge 0 fp ge 0

α uminus u+( 1113857 _uge 0 fp le 0

α uminus uminus( 1113857 _ule 0 fp ge 0

minusαβ + c

1minus e(β+c) uminusuminus( )1113876 1113877 _ule 0 fp le 0

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(14)

+erefore according to (8) and (14) the damping forceof the STMR damper can be ultimately expressed as


f

k1 + kbs( )u + k3u3 + c _u + λ

αβ + c

1minus eminus(β+c) uminusu+( )[ ] _uge 0 fp ge 0

k1 + kbs( )u + k3u3 + c _u + λα uminus u+( ) _uge 0 fp le 0

k1 + kbs( )u + k3u3 + c _u + λα uminus uminus( ) _ule 0 fp ge 0

k1 + kbs( )u + k3u3 + c _u + λ

minusαβ + c

1minus e(β+c) uminusuminus( )[ ] _ule 0 fp le 0

(15)

As a result the stiness coecurrencients k1 and k3 thedamping coecurrencient c and the ratio coecurrencient λ are ex-panded from (9)ndash(12) respectively

Marquardt algorithm was adopted to carry out the pa-rameter identication on the damping mechanical model ofthe STMR damper Low frequency and small displacementexperimental data were selected among which the excitationfrequency was 01Hz the amplitude was 5mm and thecurrent input was 0A 1A 2A and 3A respectively Fromthe experimental data it can be perceived that the laggingdisplacement in both positive and negative directions is2mm whereas 14 parameters based on the symmetric dy-namic hysteretic mechanical model were identied eidentication results are listed in Table 5 Figure 12 displaysthe comparison between the dynamic hysteresis experi-mental curves of the STMR damper and the model hysteresiscurve acquired by parameter identication presenting thatthe model curve stands in good agreement with the ex-perimental data which further validates the correctness ofthe multiparameter and symmetric dynamic hystereticmodel and indicates that the method of parameter iden-tication is eective

5 Conclusions

In this work a novel STMR damper with rate sensitivecharacteristic (speed locking) and semiactive controllingproperty was designed and fabricated based on multi-functional composite MRSPs Both the mechanicalproperties of MRSPs and the STMR damper were ex-perimentally investigated Firstly the MRSP 5 and MRSP0 samples exhibited the best magnetorheological eectand relative shear stiening eect respectively whichwere chosen as the llers of the main cylinder and ac-cessory cylinder Secondly through slow and fast ex-periments the STMR damper presented an obvious ratesensitive property and realized the speed locking func-tion in a short time and distance when external excitationrate was fast enough Besides dynamic experiment re-sults indicated that the damping force of the STMRdamper could be controlled by the excitation frequencyand the applied magnetic eld Finally a multiparameterand symmetry hysteretic model was proposed to describethe dynamic hysteretic behavior of the STMR damperwhich agreed well with the experimental data

Table 5 Results of the parameter identication

Parameters I 0A I 1A I 2A I 3Ak10 minus015 minus000049 535 minus4887k11 3359 585 minus1303 2970k12 minus5771 minus8202 1416 minus103k30 045 0022 025 minus014k31 minus043 0027 minus034 009c0 minus4523 23850 6114 30736c1 14315 031 6555 minus9370λ0 000083 094 201 minus145λ1 2320 6074 255 2609α 123 135 038 102β 0033 0022 050 001λ 0033 0022 050 001n 1 1 1 1kbs 040 040 040 040

200

150

100

50

0

ndash50

ndash100

ndash150

ndash200

Dam

ping

forc

e (kN

)


0 A experimental data1 A experimental data2 A experimental data

3 A experimental dataModel curve

Figure 12 e relationship between the model curve and ex-perimental data of the STMR damper


Conflicts of Interest

+e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

+is work was supported by Primary Research and Devel-opment Plan of Jiangsu Province (Grant no BE2017167)Natural Science Foundation of Zhejiang Province (Grant noLY15E080015) National Natural Science Foundation ofChina (Grant no 51508237) Natural Science Foundation ofJiangsu Province (Grant no BK20140560) and ResearchFoundation for Advanced Talents of Jiangsu University(Grant no 14JDG161)

References

[1] F Guo C B Du G J Yu and R P Li ldquo+e static anddynamic mechanical properties of magnetorheological sillyputtyrdquo Advances in Materials Science and Engineering vol2016 Article ID 7079698 11 pages 2016

[2] X Z Zhang W H Li and X L Gong ldquoStudy on magne-torheological shear stiffening fluidrdquo Smart Materials andStructures vol 17 no 1 p 015051 2008

[3] G R Peng W H Li T F Tian J Ding and M NakanoldquoExperimental andmodeling study of viscoelastic behaviors ofmagneto-rheological shear stiffening fluidsrdquo Korea-AustraliaRheology Journal vol 26 no 2 pp 149ndash158 2014

[4] S Wang W Jiang W Jiang et al ldquoMultifunctional polymercomposite with excellent shear stiffening performance andmagnetorheological effectrdquo Journal of Materials Chemistry Cvol 2 no 34 pp 7133ndash7140 2014

[5] Y Wang S Wang C Xu S Xuan W Jiang and X GongldquoDynamic behavior of magnetically responsive shear-stiffeninggel under high strain raterdquo Composites Science and Technologyvol 127 pp 169ndash176 2016

[6] B Sapinski ldquoParametric identification of MR linear auto-motive size damperrdquo Journal of eoretical and AppliedMechanics vol 40 no 3 pp 703ndash722 2002

[7] W L Qu S Q Qin J W Tu et al ldquoIntelligent control forbraking-induced longitudinal vibration responses of floating-type railway bridgesrdquo Smart Materials and Structures vol 18no 12 p 125003 2009

[8] W L Qu J Liu J W Tu M Run and H Cheng ldquoCrucialtechniques for design of 500 kN large-scale MR damperrdquoEarthquake Engineering and Engineering Vibration vol 27no 2 pp 124ndash130 2007 in Chinese

[9] W L Qu M Run and J W Tu ldquoDesign and simulation ofa new full scale MR damperrdquo Journal of Wuhan University ofTechnology vol 29 no 2 pp 87ndash90 2007 in Chinese

[10] W L Qu S Q Qin J W Tu J Liu and Q Zhou ldquo+eory andcrucial technologies of intelligent control for response in deckand towers of Wuhan Tianxingzhou cable-stayed bridgesubjected to train brakingrdquo China Civil Engineering Journalvol 43 no 8 pp 63ndash72 2010 in Chinese

[11] G J Yu C B Du and T Sun ldquo+ermodynamic behaviors ofa kind of self-decoupling magnetorheological damperrdquo Shockand Vibration vol 2015 Article ID 502747 9 pages 2015

[12] G J Yu C B Du and F X Wan ldquoDesign and experimentalstudies on self-decoupling magneto-rheological damperrdquoJournal of Vibration Measurement and Diagnosis vol 32no 3 pp 426ndash431 2012 in Chinese

[13] G J Yu and C B Du ldquoDesign and experimental studies oncomposite magneto-rheological damperrdquo Chinese Quarterlyof Mechanics vol 35 no 1 pp 131ndash138 2014 in Chinese

[14] G J Yu T Sun B Su et al ldquoResearch of architecturalstructures semi-active control based on SDMR damperrdquoJournal of Chongqing University of Technology (Nature Sci-ence) vol 29 no 11 pp 42ndash50 2015 in Chinese

[15] X Z Zhang W H Li and X L Gong ldquo+e rheology of shearstiffening fluid (STF) and the dynamic performance of anSTF-filled damperrdquo Smart Materials and Structures vol 17no 3 p 035027 2008

[16] H Zhou C Y Guo L H Zong et al ldquoPerformance of shearstiffening fluid and a damper as its applicationrdquo Journal ofVibration and Shock vol 32 no 18 pp 15ndash20 2013 inChinese

[17] J Liang and X H Zhang ldquoRheological properties of SP inshock transmission applicationrdquo Journal of Materials in CivilEngineering vol 27 no 9 p 04014250 2015

[18] L C Davis ldquoModel of magnetorheological elastomersrdquoJournal of Applied Physics vol 85 no 6 pp 3348ndash3351 1999

[19] AASHTO AASHTO LRFD Bridge Construction SpecificationsAmerican Association of State Highway and TransportationOfficials Washington DC USA 2012

[20] C Collette G Kroll G Saive V Guillemier and M AvraamldquoOn magnetorheologic elastomers for vibration isolationdamping and stress reduction in mass-varying structuresrdquoJournal of Intelligent Material Systems and Structures vol 21no 15 pp 1463ndash1469 2010


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ate

ria

ls


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Submit your manuscripts atwwwhindawicom

+e single shear thickening material is used as energydissipation fillers for small passive ST dampers Zhang et aldeveloped a speed-driven damper based on the shearthickening fluid and studied the dynamic performance of theST damper through both experiment and theory methods[15]+ese results confirm that the STdamper presents higherstiffness and damping at high-speed dynamic loading thanthose at low-speed loading and absorbs more energy Zhouet al developed a double-out rod-type ST damper filled byshear thickening fluid of a high-concentration polystyrene-ethyl acrylate nanometer particle suspension +e dynamicalexperiment results reveal that with the increase in excitationfrequency the storage modulus and energy dissipationmodulus rapidly increase and the output of the ST damperdramatically boosts exhibiting great absorption and energydissipation capacity the maximum energy dissipationmodulus reached up to 21 kPa [16] +e most common ap-plication of shear thickening materials in civil engineeringstructures is the shock transmission unit (STU) which isa device resembling a speed switch It is basically approxi-mating to a general damper in appearance and internalstructure which is composed of a piston and cylinder andregarded as a special damper Silly Putty has becomea promising material for the special damper of STU which iswidely used in the multispan bridge [17]

+e MR damper is the most mature energy dissipationdevice in the field of magnetorheological vibration dampingFrom the point of energy the principle of the work is tochange the energy spectrum of the vibration sourcersquos ex-citation to the system and reduce the passed energy tosuppress the vibration However in the face of huge in-centive loads the vibration damping which the MR damperdepends on does not slow down the deformation or evendestruction of civil engineering structures due to insufficientstiffness besides the mechanism of damping is relativelysimple In addition these MR dampers all belong to activedevices whichmeans that in the event of a circuit failure thatcannot be controlled by a magnetic field the damper losesthe significance of the semiactive vibration control +ecurrent solutions include setting a permanent magnet tomake the magnetorheological fluid in the MR damperproduce certain yield strength but the scheme makes thedesign of the damper more complex Furthermore com-monly used permanent magnets are made of NdFeBmaterialwith strong temperature instability meaning that the higherthe temperature the faster the demagnetization +e shearthickening material is mainly used in caging devices in-cluding all kinds of speed locking devices in order to im-prove the overall stiffness of the structure and achieve thepurpose of seismic resistance and vibration reduction At themoment researchers of the world only focus on the study ofthe mechanisms of magnetorheological damping and shearthickening damping respectively and there is no in-tersection between each other However there are no rel-evant studies that combine the characteristics of two kinds ofintelligent materials as a whole to explore new intelligentdampers with double vibration damping mechanisms

In this work a novel shear thickening magneto-rheological (STMR) damper was designed and fabricated

based onMRSPs Compared with traditionalMR dampers theSTMR damper not only exhibited controllable characteristicsof damping force under the adjustment of the magnetic fieldbut also provided a ldquolockingrdquo function under an unexpectedsudden rare load which was more suitable for the vibrationcontrol of large civil engineering structures In order to verifythe dual vibration damping characteristics of the STMRdamper slow fast and dynamic mechanical property ex-periments were carried out Finally a multiparameter andsymmetry model was established and deduced to describe thedynamic hysteretic behavior of the STMR damper

2 Experimental Section of MRSPs

21 Materials +e Dow Corning 3179 dilatant compoundwhich was purchased from Dow Corning Co Ltd was usedas the Silly Putty matrix +e composition of the Silly Puttymatrix is outlined in Table 1 Polydimethylsiloxane (PDMS)as a commonly used organic silicon material is the majorconstituent of the composition +e soft magnetic particles ofthe carbonyl iron (CI) with an average size of 35 μm werepurchased from Jiangsu Tianyi Ultra-fine metal powder CoLtd (Xuyi China)

22 Preparation and Testing of MRSPs +e dilatant com-pound as matrix and the different volume fractions of CI asfillers were homogeneously mixed using a two-roll mill(Nantong Hailite Rubber Machinery Inc China XK-160model) at room temperature For the mechanical mixingmethod up to six different volume fractions were consideredfor the present study 0 698 1011 1584 2080 and 2729+e prepared samples were marked as MRSP 0 MRSP 1MRSP 2 MRSP 3 MRSP 4 and MRSP 5 in sequence In thiswork the dynamic rheological properties of theMRSP sampleswere carried out using a commercial rheometer (Physica MCR302 Anton Paar Co Austria) During the testing procedurea parallel plate PP20 with a diameter of approximately 20mmwas used and a gap of 1mmwasmaintained at all times At thesame time a controllable magnetic field was generated by anexternal coil Besides all the samples for the experiment weremaintained at an approximately same volume value+eMRSPsample and MCR 302 rheometer are displayed in Figure 1

3 Experimental Section of the STMR Damper

31 Designing of STMRDamper +e structure of the STMRdamper is shown in Figure 2 with its appearance

Table 1 Composition of the Silly Putty matrix

Composition Weight percentagePolydimethylsiloxane (PDMS) 65Silica 17+ixotrol 9Boric acid 4Glycerine 1Titanium dioxide 1Dimethyl cyclosiloxane 1








(a) (b)





Gran G0 1 + 25ϕ + 141ϕ2( ) (1)


32

33

31

30

29

28

27

26

25

24

23

22

21

20

19

18

17

16

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15






1Front end cover30

8Screw29

1Main piston 328


1Coil26





1Semiring sleeve21

2Semiring20

2Sleeve baffle19



4Pull rod bolt 216

1Back end cover15




4Butterfly spring11




1Main piston 27

1Coil sleeve6

1Main piston 15


4Pull rod bolt 13

1Piston rod2








Gprimemintimes 100

(2)











06

05

04

03

02

01

00

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


0 T0102 T0211 T

0321 T0430 T

0533 T0627 T

(a)

12

10

08

06

04

02

00

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


0 T0102 T0211 T

0321 T0430 T

0533 T0627 T

(b)

0 20 40 60 80 100

14

16

18

12

10

08

04

02

00

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


0 T0102 T0211 T

0321 T0430 T

0533 T0627 T

(c)

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


2624222018161412100806040200

0 T0102 T0211 T

0321 T0430 T

0533 T0627 T

(d)

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


2624222018161412100806040200

0 T0102 T0211 T

0321 T0430 T

0533 T0627 T

(e)








MRSP 1

0 0287 000346 028354 8194800102 0349 001620 033280 2054320211 0480 006410 041590 648830321 0566 010900 045700 419270430 0603 013400 046900 3500533 0618 014400 047400 329170627 0627 015000 047700 318

MRSP 2

0 0309 000531 030369 5719210102 0383 003550 034750 978870211 0873 022900 064400 281220321 1060 037000 069000 186490430 1160 044000 072000 163640533 1190 045900 073100 159260627 1200 047100 072900 15478

MRSP 3

0 0411 00131 039790 3037400102 0924 02900 063400 218620211 1280 06690 061100 91330321 1500 09190 058100 63220430 1610 10400 057000 54810533 1670 10900 058000 53210627 1710 11300 058000 5133

MRSP 4

0 044 00228 041720 1829820102 124 0366 087400 238800211 190 119 071 59660321 214 159 055 34590430 224 177 047 26550533 231 186 045 24190627 231 192 039 2031

MRSP 5

0 051 00239 04861 2033890102 167 0814 08560 105160211 215 167 048 28740321 229 195 034 17440430 232 204 028 13730533 233 208 025 12020627 234 212 022 1038






Gprimemintimes 100

(3)






γ = 5γ = 10 γ = 1

γ = 05

020

018

016

014

012

010

008

006

004

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


(a)

γ = 5γ = 10 γ = 1

γ = 05

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


036034032030028026024022020018016014012010008006004

(b)

γ = 5γ = 10 γ = 1

γ = 05

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


12

10

08

06

04

02

00

(c)

γ = 5γ = 10 γ = 1

γ = 05

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


18

16

14

12

10

08

04

06

02

00

(d)

γ = 5γ = 10 γ = 1

γ = 05


Shea

r sto

rage

mod

ulus

Gprime (

MPa

) 18

20

16

14

12

10

08

04

06

02

00

(e)







100

80

60

40

20

Forc

e (kN

)



Elastic region


0 10 20 30 40 50

70

65

60

55

50

45

40

35

30

25

Stiff

ness

K (k

Nm

m)

Velocity v (mmmin)

066 mms

033 mms

083 mms

0166 mms

0083 mms

0033 mms



SamplesShearstrain

c

Gprimemax(MPa)

Gprimemin(MPa)

AMRe(MPa)

RMRe()

MRSP 1

05 0184 00666 01174 176281 0167 00619 01051 169795 0119 00547 00643 1175510 0100 00393 00607 15445

MRSP 2

05 0340 00796 02604 327141 0281 00692 02118 306075 0169 00590 01100 1864410 0135 00398 00952 23920

MRSP 3

05 1120 02770 08430 304331 0934 02390 06950 290795 0484 01150 03690 3208710 0340 00498 02902 58273

MRSP 4

05 1630 04020 12280 305471 1360 03530 10070 285275 0735 02010 05340 2656710 0480 00669 04131 61749

MRSP 5

05 1960 04340 15260 351611 1770 03660 14040 383615 0907 02140 06930 3238310 0592 00843 05077 60225


300

250

200

150

100

50

0

Forc

e (kN

)Lock distance

10 mms

8 mms

6 mms









Displacement (mm)

300250200150100

500


Dam

ping

forc

e (kN

)


01 Hz05 Hz10 Hz

15 Hz25 Hz



200

150

100

50

0

ndash50

ndash100

ndash150

ndash200

Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(a)

200250300

150100

500


Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(b)

200250300

150100

500


Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(c)

300

200

100

0

ndash100

ndash200

ndash300

Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(d)

300

200

100

0

ndash100

ndash200

ndash300

Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(e)








11138681113868111386811138681113868

11138681113868111386811138681113868nminus c| _u|fp fp

11138681113868111386811138681113868

11138681113868111386811138681113868nminus1


11138681113868111386811138681113868

11138681113868111386811138681113868n

1113882 1113883 _u(5)






fbs kbsu (7)




+ c _u + λfp

(8)




k1 k10 He( 1113857 + k11 He( 1113857| _u| + k12 He( 1113857| _u|2 (9)

k3 k30 He( 1113857 + k31 He( 1113857| _u| (10)

c c0 He( 1113857 + c1 He( 1113857| _u| (11)

λ λ0 He( 1113857 + λ1 He( 1113857| _u| (12)



F1 fp1113872 1113873 uminus u+

F2 fp1113872 1113873 uminus u+







(13)


fp

αβ + c




minusαβ + c


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(14)



f

k1 + kbs( )u + k3u3 + c _u + λ

αβ + c




k1 + kbs( )u + k3u3 + c _u + λ

minusαβ + c


(15)



5 Conclusions




200

150

100

50

0

ndash50

ndash100

ndash150

ndash200

Dam

ping

forc

e (kN

)








Acknowledgments


References
























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls










(a) (b)





Gran G0 1 + 25ϕ + 141ϕ2( ) (1)


32

33

31

30

29

28

27

26

25

24

23

22

21

20

19

18

17

16

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15






1Front end cover30

8Screw29

1Main piston 328


1Coil26





1Semiring sleeve21

2Semiring20

2Sleeve baffle19



4Pull rod bolt 216

1Back end cover15




4Butterfly spring11




1Main piston 27

1Coil sleeve6

1Main piston 15


4Pull rod bolt 13

1Piston rod2








Gprimemintimes 100

(2)











06

05

04

03

02

01

00

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


0 T0102 T0211 T

0321 T0430 T

0533 T0627 T

(a)

12

10

08

06

04

02

00

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


0 T0102 T0211 T

0321 T0430 T

0533 T0627 T

(b)

0 20 40 60 80 100

14

16

18

12

10

08

04

02

00

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


0 T0102 T0211 T

0321 T0430 T

0533 T0627 T

(c)

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


2624222018161412100806040200

0 T0102 T0211 T

0321 T0430 T

0533 T0627 T

(d)

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


2624222018161412100806040200

0 T0102 T0211 T

0321 T0430 T

0533 T0627 T

(e)








MRSP 1

0 0287 000346 028354 8194800102 0349 001620 033280 2054320211 0480 006410 041590 648830321 0566 010900 045700 419270430 0603 013400 046900 3500533 0618 014400 047400 329170627 0627 015000 047700 318

MRSP 2

0 0309 000531 030369 5719210102 0383 003550 034750 978870211 0873 022900 064400 281220321 1060 037000 069000 186490430 1160 044000 072000 163640533 1190 045900 073100 159260627 1200 047100 072900 15478

MRSP 3

0 0411 00131 039790 3037400102 0924 02900 063400 218620211 1280 06690 061100 91330321 1500 09190 058100 63220430 1610 10400 057000 54810533 1670 10900 058000 53210627 1710 11300 058000 5133

MRSP 4

0 044 00228 041720 1829820102 124 0366 087400 238800211 190 119 071 59660321 214 159 055 34590430 224 177 047 26550533 231 186 045 24190627 231 192 039 2031

MRSP 5

0 051 00239 04861 2033890102 167 0814 08560 105160211 215 167 048 28740321 229 195 034 17440430 232 204 028 13730533 233 208 025 12020627 234 212 022 1038






Gprimemintimes 100

(3)






γ = 5γ = 10 γ = 1

γ = 05

020

018

016

014

012

010

008

006

004

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


(a)

γ = 5γ = 10 γ = 1

γ = 05

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


036034032030028026024022020018016014012010008006004

(b)

γ = 5γ = 10 γ = 1

γ = 05

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


12

10

08

06

04

02

00

(c)

γ = 5γ = 10 γ = 1

γ = 05

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


18

16

14

12

10

08

04

06

02

00

(d)

γ = 5γ = 10 γ = 1

γ = 05


Shea

r sto

rage

mod

ulus

Gprime (

MPa

) 18

20

16

14

12

10

08

04

06

02

00

(e)







100

80

60

40

20

Forc

e (kN

)



Elastic region


0 10 20 30 40 50

70

65

60

55

50

45

40

35

30

25

Stiff

ness

K (k

Nm

m)

Velocity v (mmmin)

066 mms

033 mms

083 mms

0166 mms

0083 mms

0033 mms



SamplesShearstrain

c

Gprimemax(MPa)

Gprimemin(MPa)

AMRe(MPa)

RMRe()

MRSP 1

05 0184 00666 01174 176281 0167 00619 01051 169795 0119 00547 00643 1175510 0100 00393 00607 15445

MRSP 2

05 0340 00796 02604 327141 0281 00692 02118 306075 0169 00590 01100 1864410 0135 00398 00952 23920

MRSP 3

05 1120 02770 08430 304331 0934 02390 06950 290795 0484 01150 03690 3208710 0340 00498 02902 58273

MRSP 4

05 1630 04020 12280 305471 1360 03530 10070 285275 0735 02010 05340 2656710 0480 00669 04131 61749

MRSP 5

05 1960 04340 15260 351611 1770 03660 14040 383615 0907 02140 06930 3238310 0592 00843 05077 60225


300

250

200

150

100

50

0

Forc

e (kN

)Lock distance

10 mms

8 mms

6 mms









Displacement (mm)

300250200150100

500


Dam

ping

forc

e (kN

)


01 Hz05 Hz10 Hz

15 Hz25 Hz



200

150

100

50

0

ndash50

ndash100

ndash150

ndash200

Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(a)

200250300

150100

500


Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(b)

200250300

150100

500


Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(c)

300

200

100

0

ndash100

ndash200

ndash300

Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(d)

300

200

100

0

ndash100

ndash200

ndash300

Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(e)








11138681113868111386811138681113868

11138681113868111386811138681113868nminus c| _u|fp fp

11138681113868111386811138681113868

11138681113868111386811138681113868nminus1


11138681113868111386811138681113868

11138681113868111386811138681113868n

1113882 1113883 _u(5)






fbs kbsu (7)




+ c _u + λfp

(8)




k1 k10 He( 1113857 + k11 He( 1113857| _u| + k12 He( 1113857| _u|2 (9)

k3 k30 He( 1113857 + k31 He( 1113857| _u| (10)

c c0 He( 1113857 + c1 He( 1113857| _u| (11)

λ λ0 He( 1113857 + λ1 He( 1113857| _u| (12)



F1 fp1113872 1113873 uminus u+

F2 fp1113872 1113873 uminus u+







(13)


fp

αβ + c




minusαβ + c


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(14)



f

k1 + kbs( )u + k3u3 + c _u + λ

αβ + c




k1 + kbs( )u + k3u3 + c _u + λ

minusαβ + c


(15)



5 Conclusions




200

150

100

50

0

ndash50

ndash100

ndash150

ndash200

Dam

ping

forc

e (kN

)








Acknowledgments


References
























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls






Gran G0 1 + 25ϕ + 141ϕ2( ) (1)


32

33

31

30

29

28

27

26

25

24

23

22

21

20

19

18

17

16

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15






1Front end cover30

8Screw29

1Main piston 328


1Coil26





1Semiring sleeve21

2Semiring20

2Sleeve baffle19



4Pull rod bolt 216

1Back end cover15




4Butterfly spring11




1Main piston 27

1Coil sleeve6

1Main piston 15


4Pull rod bolt 13

1Piston rod2








Gprimemintimes 100

(2)











06

05

04

03

02

01

00

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


0 T0102 T0211 T

0321 T0430 T

0533 T0627 T

(a)

12

10

08

06

04

02

00

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


0 T0102 T0211 T

0321 T0430 T

0533 T0627 T

(b)

0 20 40 60 80 100

14

16

18

12

10

08

04

02

00

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


0 T0102 T0211 T

0321 T0430 T

0533 T0627 T

(c)

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


2624222018161412100806040200

0 T0102 T0211 T

0321 T0430 T

0533 T0627 T

(d)

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


2624222018161412100806040200

0 T0102 T0211 T

0321 T0430 T

0533 T0627 T

(e)








MRSP 1

0 0287 000346 028354 8194800102 0349 001620 033280 2054320211 0480 006410 041590 648830321 0566 010900 045700 419270430 0603 013400 046900 3500533 0618 014400 047400 329170627 0627 015000 047700 318

MRSP 2

0 0309 000531 030369 5719210102 0383 003550 034750 978870211 0873 022900 064400 281220321 1060 037000 069000 186490430 1160 044000 072000 163640533 1190 045900 073100 159260627 1200 047100 072900 15478

MRSP 3

0 0411 00131 039790 3037400102 0924 02900 063400 218620211 1280 06690 061100 91330321 1500 09190 058100 63220430 1610 10400 057000 54810533 1670 10900 058000 53210627 1710 11300 058000 5133

MRSP 4

0 044 00228 041720 1829820102 124 0366 087400 238800211 190 119 071 59660321 214 159 055 34590430 224 177 047 26550533 231 186 045 24190627 231 192 039 2031

MRSP 5

0 051 00239 04861 2033890102 167 0814 08560 105160211 215 167 048 28740321 229 195 034 17440430 232 204 028 13730533 233 208 025 12020627 234 212 022 1038






Gprimemintimes 100

(3)






γ = 5γ = 10 γ = 1

γ = 05

020

018

016

014

012

010

008

006

004

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


(a)

γ = 5γ = 10 γ = 1

γ = 05

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


036034032030028026024022020018016014012010008006004

(b)

γ = 5γ = 10 γ = 1

γ = 05

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


12

10

08

06

04

02

00

(c)

γ = 5γ = 10 γ = 1

γ = 05

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


18

16

14

12

10

08

04

06

02

00

(d)

γ = 5γ = 10 γ = 1

γ = 05


Shea

r sto

rage

mod

ulus

Gprime (

MPa

) 18

20

16

14

12

10

08

04

06

02

00

(e)







100

80

60

40

20

Forc

e (kN

)



Elastic region


0 10 20 30 40 50

70

65

60

55

50

45

40

35

30

25

Stiff

ness

K (k

Nm

m)

Velocity v (mmmin)

066 mms

033 mms

083 mms

0166 mms

0083 mms

0033 mms



SamplesShearstrain

c

Gprimemax(MPa)

Gprimemin(MPa)

AMRe(MPa)

RMRe()

MRSP 1

05 0184 00666 01174 176281 0167 00619 01051 169795 0119 00547 00643 1175510 0100 00393 00607 15445

MRSP 2

05 0340 00796 02604 327141 0281 00692 02118 306075 0169 00590 01100 1864410 0135 00398 00952 23920

MRSP 3

05 1120 02770 08430 304331 0934 02390 06950 290795 0484 01150 03690 3208710 0340 00498 02902 58273

MRSP 4

05 1630 04020 12280 305471 1360 03530 10070 285275 0735 02010 05340 2656710 0480 00669 04131 61749

MRSP 5

05 1960 04340 15260 351611 1770 03660 14040 383615 0907 02140 06930 3238310 0592 00843 05077 60225


300

250

200

150

100

50

0

Forc

e (kN

)Lock distance

10 mms

8 mms

6 mms









Displacement (mm)

300250200150100

500


Dam

ping

forc

e (kN

)


01 Hz05 Hz10 Hz

15 Hz25 Hz



200

150

100

50

0

ndash50

ndash100

ndash150

ndash200

Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(a)

200250300

150100

500


Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(b)

200250300

150100

500


Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(c)

300

200

100

0

ndash100

ndash200

ndash300

Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(d)

300

200

100

0

ndash100

ndash200

ndash300

Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(e)








11138681113868111386811138681113868

11138681113868111386811138681113868nminus c| _u|fp fp

11138681113868111386811138681113868

11138681113868111386811138681113868nminus1


11138681113868111386811138681113868

11138681113868111386811138681113868n

1113882 1113883 _u(5)






fbs kbsu (7)




+ c _u + λfp

(8)




k1 k10 He( 1113857 + k11 He( 1113857| _u| + k12 He( 1113857| _u|2 (9)

k3 k30 He( 1113857 + k31 He( 1113857| _u| (10)

c c0 He( 1113857 + c1 He( 1113857| _u| (11)

λ λ0 He( 1113857 + λ1 He( 1113857| _u| (12)



F1 fp1113872 1113873 uminus u+

F2 fp1113872 1113873 uminus u+







(13)


fp

αβ + c




minusαβ + c


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(14)



f

k1 + kbs( )u + k3u3 + c _u + λ

αβ + c




k1 + kbs( )u + k3u3 + c _u + λ

minusαβ + c


(15)



5 Conclusions




200

150

100

50

0

ndash50

ndash100

ndash150

ndash200

Dam

ping

forc

e (kN

)








Acknowledgments


References
























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls








Gprimemintimes 100

(2)











06

05

04

03

02

01

00

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


0 T0102 T0211 T

0321 T0430 T

0533 T0627 T

(a)

12

10

08

06

04

02

00

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


0 T0102 T0211 T

0321 T0430 T

0533 T0627 T

(b)

0 20 40 60 80 100

14

16

18

12

10

08

04

02

00

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


0 T0102 T0211 T

0321 T0430 T

0533 T0627 T

(c)

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


2624222018161412100806040200

0 T0102 T0211 T

0321 T0430 T

0533 T0627 T

(d)

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


2624222018161412100806040200

0 T0102 T0211 T

0321 T0430 T

0533 T0627 T

(e)








MRSP 1

0 0287 000346 028354 8194800102 0349 001620 033280 2054320211 0480 006410 041590 648830321 0566 010900 045700 419270430 0603 013400 046900 3500533 0618 014400 047400 329170627 0627 015000 047700 318

MRSP 2

0 0309 000531 030369 5719210102 0383 003550 034750 978870211 0873 022900 064400 281220321 1060 037000 069000 186490430 1160 044000 072000 163640533 1190 045900 073100 159260627 1200 047100 072900 15478

MRSP 3

0 0411 00131 039790 3037400102 0924 02900 063400 218620211 1280 06690 061100 91330321 1500 09190 058100 63220430 1610 10400 057000 54810533 1670 10900 058000 53210627 1710 11300 058000 5133

MRSP 4

0 044 00228 041720 1829820102 124 0366 087400 238800211 190 119 071 59660321 214 159 055 34590430 224 177 047 26550533 231 186 045 24190627 231 192 039 2031

MRSP 5

0 051 00239 04861 2033890102 167 0814 08560 105160211 215 167 048 28740321 229 195 034 17440430 232 204 028 13730533 233 208 025 12020627 234 212 022 1038






Gprimemintimes 100

(3)






γ = 5γ = 10 γ = 1

γ = 05

020

018

016

014

012

010

008

006

004

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


(a)

γ = 5γ = 10 γ = 1

γ = 05

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


036034032030028026024022020018016014012010008006004

(b)

γ = 5γ = 10 γ = 1

γ = 05

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


12

10

08

06

04

02

00

(c)

γ = 5γ = 10 γ = 1

γ = 05

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


18

16

14

12

10

08

04

06

02

00

(d)

γ = 5γ = 10 γ = 1

γ = 05


Shea

r sto

rage

mod

ulus

Gprime (

MPa

) 18

20

16

14

12

10

08

04

06

02

00

(e)







100

80

60

40

20

Forc

e (kN

)



Elastic region


0 10 20 30 40 50

70

65

60

55

50

45

40

35

30

25

Stiff

ness

K (k

Nm

m)

Velocity v (mmmin)

066 mms

033 mms

083 mms

0166 mms

0083 mms

0033 mms



SamplesShearstrain

c

Gprimemax(MPa)

Gprimemin(MPa)

AMRe(MPa)

RMRe()

MRSP 1

05 0184 00666 01174 176281 0167 00619 01051 169795 0119 00547 00643 1175510 0100 00393 00607 15445

MRSP 2

05 0340 00796 02604 327141 0281 00692 02118 306075 0169 00590 01100 1864410 0135 00398 00952 23920

MRSP 3

05 1120 02770 08430 304331 0934 02390 06950 290795 0484 01150 03690 3208710 0340 00498 02902 58273

MRSP 4

05 1630 04020 12280 305471 1360 03530 10070 285275 0735 02010 05340 2656710 0480 00669 04131 61749

MRSP 5

05 1960 04340 15260 351611 1770 03660 14040 383615 0907 02140 06930 3238310 0592 00843 05077 60225


300

250

200

150

100

50

0

Forc

e (kN

)Lock distance

10 mms

8 mms

6 mms









Displacement (mm)

300250200150100

500


Dam

ping

forc

e (kN

)


01 Hz05 Hz10 Hz

15 Hz25 Hz



200

150

100

50

0

ndash50

ndash100

ndash150

ndash200

Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(a)

200250300

150100

500


Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(b)

200250300

150100

500


Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(c)

300

200

100

0

ndash100

ndash200

ndash300

Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(d)

300

200

100

0

ndash100

ndash200

ndash300

Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(e)








11138681113868111386811138681113868

11138681113868111386811138681113868nminus c| _u|fp fp

11138681113868111386811138681113868

11138681113868111386811138681113868nminus1


11138681113868111386811138681113868

11138681113868111386811138681113868n

1113882 1113883 _u(5)






fbs kbsu (7)




+ c _u + λfp

(8)




k1 k10 He( 1113857 + k11 He( 1113857| _u| + k12 He( 1113857| _u|2 (9)

k3 k30 He( 1113857 + k31 He( 1113857| _u| (10)

c c0 He( 1113857 + c1 He( 1113857| _u| (11)

λ λ0 He( 1113857 + λ1 He( 1113857| _u| (12)



F1 fp1113872 1113873 uminus u+

F2 fp1113872 1113873 uminus u+







(13)


fp

αβ + c




minusαβ + c


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(14)



f

k1 + kbs( )u + k3u3 + c _u + λ

αβ + c




k1 + kbs( )u + k3u3 + c _u + λ

minusαβ + c


(15)



5 Conclusions




200

150

100

50

0

ndash50

ndash100

ndash150

ndash200

Dam

ping

forc

e (kN

)








Acknowledgments


References
























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls




06

05

04

03

02

01

00

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


0 T0102 T0211 T

0321 T0430 T

0533 T0627 T

(a)

12

10

08

06

04

02

00

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


0 T0102 T0211 T

0321 T0430 T

0533 T0627 T

(b)

0 20 40 60 80 100

14

16

18

12

10

08

04

02

00

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


0 T0102 T0211 T

0321 T0430 T

0533 T0627 T

(c)

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


2624222018161412100806040200

0 T0102 T0211 T

0321 T0430 T

0533 T0627 T

(d)

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


2624222018161412100806040200

0 T0102 T0211 T

0321 T0430 T

0533 T0627 T

(e)








MRSP 1

0 0287 000346 028354 8194800102 0349 001620 033280 2054320211 0480 006410 041590 648830321 0566 010900 045700 419270430 0603 013400 046900 3500533 0618 014400 047400 329170627 0627 015000 047700 318

MRSP 2

0 0309 000531 030369 5719210102 0383 003550 034750 978870211 0873 022900 064400 281220321 1060 037000 069000 186490430 1160 044000 072000 163640533 1190 045900 073100 159260627 1200 047100 072900 15478

MRSP 3

0 0411 00131 039790 3037400102 0924 02900 063400 218620211 1280 06690 061100 91330321 1500 09190 058100 63220430 1610 10400 057000 54810533 1670 10900 058000 53210627 1710 11300 058000 5133

MRSP 4

0 044 00228 041720 1829820102 124 0366 087400 238800211 190 119 071 59660321 214 159 055 34590430 224 177 047 26550533 231 186 045 24190627 231 192 039 2031

MRSP 5

0 051 00239 04861 2033890102 167 0814 08560 105160211 215 167 048 28740321 229 195 034 17440430 232 204 028 13730533 233 208 025 12020627 234 212 022 1038






Gprimemintimes 100

(3)






γ = 5γ = 10 γ = 1

γ = 05

020

018

016

014

012

010

008

006

004

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


(a)

γ = 5γ = 10 γ = 1

γ = 05

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


036034032030028026024022020018016014012010008006004

(b)

γ = 5γ = 10 γ = 1

γ = 05

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


12

10

08

06

04

02

00

(c)

γ = 5γ = 10 γ = 1

γ = 05

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


18

16

14

12

10

08

04

06

02

00

(d)

γ = 5γ = 10 γ = 1

γ = 05


Shea

r sto

rage

mod

ulus

Gprime (

MPa

) 18

20

16

14

12

10

08

04

06

02

00

(e)







100

80

60

40

20

Forc

e (kN

)



Elastic region


0 10 20 30 40 50

70

65

60

55

50

45

40

35

30

25

Stiff

ness

K (k

Nm

m)

Velocity v (mmmin)

066 mms

033 mms

083 mms

0166 mms

0083 mms

0033 mms



SamplesShearstrain

c

Gprimemax(MPa)

Gprimemin(MPa)

AMRe(MPa)

RMRe()

MRSP 1

05 0184 00666 01174 176281 0167 00619 01051 169795 0119 00547 00643 1175510 0100 00393 00607 15445

MRSP 2

05 0340 00796 02604 327141 0281 00692 02118 306075 0169 00590 01100 1864410 0135 00398 00952 23920

MRSP 3

05 1120 02770 08430 304331 0934 02390 06950 290795 0484 01150 03690 3208710 0340 00498 02902 58273

MRSP 4

05 1630 04020 12280 305471 1360 03530 10070 285275 0735 02010 05340 2656710 0480 00669 04131 61749

MRSP 5

05 1960 04340 15260 351611 1770 03660 14040 383615 0907 02140 06930 3238310 0592 00843 05077 60225


300

250

200

150

100

50

0

Forc

e (kN

)Lock distance

10 mms

8 mms

6 mms









Displacement (mm)

300250200150100

500


Dam

ping

forc

e (kN

)


01 Hz05 Hz10 Hz

15 Hz25 Hz



200

150

100

50

0

ndash50

ndash100

ndash150

ndash200

Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(a)

200250300

150100

500


Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(b)

200250300

150100

500


Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(c)

300

200

100

0

ndash100

ndash200

ndash300

Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(d)

300

200

100

0

ndash100

ndash200

ndash300

Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(e)








11138681113868111386811138681113868

11138681113868111386811138681113868nminus c| _u|fp fp

11138681113868111386811138681113868

11138681113868111386811138681113868nminus1


11138681113868111386811138681113868

11138681113868111386811138681113868n

1113882 1113883 _u(5)






fbs kbsu (7)




+ c _u + λfp

(8)




k1 k10 He( 1113857 + k11 He( 1113857| _u| + k12 He( 1113857| _u|2 (9)

k3 k30 He( 1113857 + k31 He( 1113857| _u| (10)

c c0 He( 1113857 + c1 He( 1113857| _u| (11)

λ λ0 He( 1113857 + λ1 He( 1113857| _u| (12)



F1 fp1113872 1113873 uminus u+

F2 fp1113872 1113873 uminus u+







(13)


fp

αβ + c




minusαβ + c


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(14)



f

k1 + kbs( )u + k3u3 + c _u + λ

αβ + c




k1 + kbs( )u + k3u3 + c _u + λ

minusαβ + c


(15)



5 Conclusions




200

150

100

50

0

ndash50

ndash100

ndash150

ndash200

Dam

ping

forc

e (kN

)








Acknowledgments


References
























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls









MRSP 1

0 0287 000346 028354 8194800102 0349 001620 033280 2054320211 0480 006410 041590 648830321 0566 010900 045700 419270430 0603 013400 046900 3500533 0618 014400 047400 329170627 0627 015000 047700 318

MRSP 2

0 0309 000531 030369 5719210102 0383 003550 034750 978870211 0873 022900 064400 281220321 1060 037000 069000 186490430 1160 044000 072000 163640533 1190 045900 073100 159260627 1200 047100 072900 15478

MRSP 3

0 0411 00131 039790 3037400102 0924 02900 063400 218620211 1280 06690 061100 91330321 1500 09190 058100 63220430 1610 10400 057000 54810533 1670 10900 058000 53210627 1710 11300 058000 5133

MRSP 4

0 044 00228 041720 1829820102 124 0366 087400 238800211 190 119 071 59660321 214 159 055 34590430 224 177 047 26550533 231 186 045 24190627 231 192 039 2031

MRSP 5

0 051 00239 04861 2033890102 167 0814 08560 105160211 215 167 048 28740321 229 195 034 17440430 232 204 028 13730533 233 208 025 12020627 234 212 022 1038






Gprimemintimes 100

(3)






γ = 5γ = 10 γ = 1

γ = 05

020

018

016

014

012

010

008

006

004

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


(a)

γ = 5γ = 10 γ = 1

γ = 05

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


036034032030028026024022020018016014012010008006004

(b)

γ = 5γ = 10 γ = 1

γ = 05

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


12

10

08

06

04

02

00

(c)

γ = 5γ = 10 γ = 1

γ = 05

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


18

16

14

12

10

08

04

06

02

00

(d)

γ = 5γ = 10 γ = 1

γ = 05


Shea

r sto

rage

mod

ulus

Gprime (

MPa

) 18

20

16

14

12

10

08

04

06

02

00

(e)







100

80

60

40

20

Forc

e (kN

)



Elastic region


0 10 20 30 40 50

70

65

60

55

50

45

40

35

30

25

Stiff

ness

K (k

Nm

m)

Velocity v (mmmin)

066 mms

033 mms

083 mms

0166 mms

0083 mms

0033 mms



SamplesShearstrain

c

Gprimemax(MPa)

Gprimemin(MPa)

AMRe(MPa)

RMRe()

MRSP 1

05 0184 00666 01174 176281 0167 00619 01051 169795 0119 00547 00643 1175510 0100 00393 00607 15445

MRSP 2

05 0340 00796 02604 327141 0281 00692 02118 306075 0169 00590 01100 1864410 0135 00398 00952 23920

MRSP 3

05 1120 02770 08430 304331 0934 02390 06950 290795 0484 01150 03690 3208710 0340 00498 02902 58273

MRSP 4

05 1630 04020 12280 305471 1360 03530 10070 285275 0735 02010 05340 2656710 0480 00669 04131 61749

MRSP 5

05 1960 04340 15260 351611 1770 03660 14040 383615 0907 02140 06930 3238310 0592 00843 05077 60225


300

250

200

150

100

50

0

Forc

e (kN

)Lock distance

10 mms

8 mms

6 mms









Displacement (mm)

300250200150100

500


Dam

ping

forc

e (kN

)


01 Hz05 Hz10 Hz

15 Hz25 Hz



200

150

100

50

0

ndash50

ndash100

ndash150

ndash200

Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(a)

200250300

150100

500


Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(b)

200250300

150100

500


Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(c)

300

200

100

0

ndash100

ndash200

ndash300

Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(d)

300

200

100

0

ndash100

ndash200

ndash300

Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(e)








11138681113868111386811138681113868

11138681113868111386811138681113868nminus c| _u|fp fp

11138681113868111386811138681113868

11138681113868111386811138681113868nminus1


11138681113868111386811138681113868

11138681113868111386811138681113868n

1113882 1113883 _u(5)






fbs kbsu (7)




+ c _u + λfp

(8)




k1 k10 He( 1113857 + k11 He( 1113857| _u| + k12 He( 1113857| _u|2 (9)

k3 k30 He( 1113857 + k31 He( 1113857| _u| (10)

c c0 He( 1113857 + c1 He( 1113857| _u| (11)

λ λ0 He( 1113857 + λ1 He( 1113857| _u| (12)



F1 fp1113872 1113873 uminus u+

F2 fp1113872 1113873 uminus u+







(13)


fp

αβ + c




minusαβ + c


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(14)



f

k1 + kbs( )u + k3u3 + c _u + λ

αβ + c




k1 + kbs( )u + k3u3 + c _u + λ

minusαβ + c


(15)



5 Conclusions




200

150

100

50

0

ndash50

ndash100

ndash150

ndash200

Dam

ping

forc

e (kN

)








Acknowledgments


References
























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls








Gprimemintimes 100

(3)






γ = 5γ = 10 γ = 1

γ = 05

020

018

016

014

012

010

008

006

004

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


(a)

γ = 5γ = 10 γ = 1

γ = 05

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


036034032030028026024022020018016014012010008006004

(b)

γ = 5γ = 10 γ = 1

γ = 05

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


12

10

08

06

04

02

00

(c)

γ = 5γ = 10 γ = 1

γ = 05

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


18

16

14

12

10

08

04

06

02

00

(d)

γ = 5γ = 10 γ = 1

γ = 05


Shea

r sto

rage

mod

ulus

Gprime (

MPa

) 18

20

16

14

12

10

08

04

06

02

00

(e)







100

80

60

40

20

Forc

e (kN

)



Elastic region


0 10 20 30 40 50

70

65

60

55

50

45

40

35

30

25

Stiff

ness

K (k

Nm

m)

Velocity v (mmmin)

066 mms

033 mms

083 mms

0166 mms

0083 mms

0033 mms



SamplesShearstrain

c

Gprimemax(MPa)

Gprimemin(MPa)

AMRe(MPa)

RMRe()

MRSP 1

05 0184 00666 01174 176281 0167 00619 01051 169795 0119 00547 00643 1175510 0100 00393 00607 15445

MRSP 2

05 0340 00796 02604 327141 0281 00692 02118 306075 0169 00590 01100 1864410 0135 00398 00952 23920

MRSP 3

05 1120 02770 08430 304331 0934 02390 06950 290795 0484 01150 03690 3208710 0340 00498 02902 58273

MRSP 4

05 1630 04020 12280 305471 1360 03530 10070 285275 0735 02010 05340 2656710 0480 00669 04131 61749

MRSP 5

05 1960 04340 15260 351611 1770 03660 14040 383615 0907 02140 06930 3238310 0592 00843 05077 60225


300

250

200

150

100

50

0

Forc

e (kN

)Lock distance

10 mms

8 mms

6 mms









Displacement (mm)

300250200150100

500


Dam

ping

forc

e (kN

)


01 Hz05 Hz10 Hz

15 Hz25 Hz



200

150

100

50

0

ndash50

ndash100

ndash150

ndash200

Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(a)

200250300

150100

500


Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(b)

200250300

150100

500


Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(c)

300

200

100

0

ndash100

ndash200

ndash300

Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(d)

300

200

100

0

ndash100

ndash200

ndash300

Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(e)








11138681113868111386811138681113868

11138681113868111386811138681113868nminus c| _u|fp fp

11138681113868111386811138681113868

11138681113868111386811138681113868nminus1


11138681113868111386811138681113868

11138681113868111386811138681113868n

1113882 1113883 _u(5)






fbs kbsu (7)




+ c _u + λfp

(8)




k1 k10 He( 1113857 + k11 He( 1113857| _u| + k12 He( 1113857| _u|2 (9)

k3 k30 He( 1113857 + k31 He( 1113857| _u| (10)

c c0 He( 1113857 + c1 He( 1113857| _u| (11)

λ λ0 He( 1113857 + λ1 He( 1113857| _u| (12)



F1 fp1113872 1113873 uminus u+

F2 fp1113872 1113873 uminus u+







(13)


fp

αβ + c




minusαβ + c


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(14)



f

k1 + kbs( )u + k3u3 + c _u + λ

αβ + c




k1 + kbs( )u + k3u3 + c _u + λ

minusαβ + c


(15)



5 Conclusions




200

150

100

50

0

ndash50

ndash100

ndash150

ndash200

Dam

ping

forc

e (kN

)








Acknowledgments


References
























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls




γ = 5γ = 10 γ = 1

γ = 05

020

018

016

014

012

010

008

006

004

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


(a)

γ = 5γ = 10 γ = 1

γ = 05

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


036034032030028026024022020018016014012010008006004

(b)

γ = 5γ = 10 γ = 1

γ = 05

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


12

10

08

06

04

02

00

(c)

γ = 5γ = 10 γ = 1

γ = 05

Shea

r sto

rage

mod

ulus

Gprime (

MPa

)


18

16

14

12

10

08

04

06

02

00

(d)

γ = 5γ = 10 γ = 1

γ = 05


Shea

r sto

rage

mod

ulus

Gprime (

MPa

) 18

20

16

14

12

10

08

04

06

02

00

(e)







100

80

60

40

20

Forc

e (kN

)



Elastic region


0 10 20 30 40 50

70

65

60

55

50

45

40

35

30

25

Stiff

ness

K (k

Nm

m)

Velocity v (mmmin)

066 mms

033 mms

083 mms

0166 mms

0083 mms

0033 mms



SamplesShearstrain

c

Gprimemax(MPa)

Gprimemin(MPa)

AMRe(MPa)

RMRe()

MRSP 1

05 0184 00666 01174 176281 0167 00619 01051 169795 0119 00547 00643 1175510 0100 00393 00607 15445

MRSP 2

05 0340 00796 02604 327141 0281 00692 02118 306075 0169 00590 01100 1864410 0135 00398 00952 23920

MRSP 3

05 1120 02770 08430 304331 0934 02390 06950 290795 0484 01150 03690 3208710 0340 00498 02902 58273

MRSP 4

05 1630 04020 12280 305471 1360 03530 10070 285275 0735 02010 05340 2656710 0480 00669 04131 61749

MRSP 5

05 1960 04340 15260 351611 1770 03660 14040 383615 0907 02140 06930 3238310 0592 00843 05077 60225


300

250

200

150

100

50

0

Forc

e (kN

)Lock distance

10 mms

8 mms

6 mms









Displacement (mm)

300250200150100

500


Dam

ping

forc

e (kN

)


01 Hz05 Hz10 Hz

15 Hz25 Hz



200

150

100

50

0

ndash50

ndash100

ndash150

ndash200

Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(a)

200250300

150100

500


Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(b)

200250300

150100

500


Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(c)

300

200

100

0

ndash100

ndash200

ndash300

Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(d)

300

200

100

0

ndash100

ndash200

ndash300

Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(e)








11138681113868111386811138681113868

11138681113868111386811138681113868nminus c| _u|fp fp

11138681113868111386811138681113868

11138681113868111386811138681113868nminus1


11138681113868111386811138681113868

11138681113868111386811138681113868n

1113882 1113883 _u(5)






fbs kbsu (7)




+ c _u + λfp

(8)




k1 k10 He( 1113857 + k11 He( 1113857| _u| + k12 He( 1113857| _u|2 (9)

k3 k30 He( 1113857 + k31 He( 1113857| _u| (10)

c c0 He( 1113857 + c1 He( 1113857| _u| (11)

λ λ0 He( 1113857 + λ1 He( 1113857| _u| (12)



F1 fp1113872 1113873 uminus u+

F2 fp1113872 1113873 uminus u+







(13)


fp

αβ + c




minusαβ + c


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(14)



f

k1 + kbs( )u + k3u3 + c _u + λ

αβ + c




k1 + kbs( )u + k3u3 + c _u + λ

minusαβ + c


(15)



5 Conclusions




200

150

100

50

0

ndash50

ndash100

ndash150

ndash200

Dam

ping

forc

e (kN

)








Acknowledgments


References
























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls








100

80

60

40

20

Forc

e (kN

)



Elastic region


0 10 20 30 40 50

70

65

60

55

50

45

40

35

30

25

Stiff

ness

K (k

Nm

m)

Velocity v (mmmin)

066 mms

033 mms

083 mms

0166 mms

0083 mms

0033 mms



SamplesShearstrain

c

Gprimemax(MPa)

Gprimemin(MPa)

AMRe(MPa)

RMRe()

MRSP 1

05 0184 00666 01174 176281 0167 00619 01051 169795 0119 00547 00643 1175510 0100 00393 00607 15445

MRSP 2

05 0340 00796 02604 327141 0281 00692 02118 306075 0169 00590 01100 1864410 0135 00398 00952 23920

MRSP 3

05 1120 02770 08430 304331 0934 02390 06950 290795 0484 01150 03690 3208710 0340 00498 02902 58273

MRSP 4

05 1630 04020 12280 305471 1360 03530 10070 285275 0735 02010 05340 2656710 0480 00669 04131 61749

MRSP 5

05 1960 04340 15260 351611 1770 03660 14040 383615 0907 02140 06930 3238310 0592 00843 05077 60225


300

250

200

150

100

50

0

Forc

e (kN

)Lock distance

10 mms

8 mms

6 mms









Displacement (mm)

300250200150100

500


Dam

ping

forc

e (kN

)


01 Hz05 Hz10 Hz

15 Hz25 Hz



200

150

100

50

0

ndash50

ndash100

ndash150

ndash200

Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(a)

200250300

150100

500


Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(b)

200250300

150100

500


Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(c)

300

200

100

0

ndash100

ndash200

ndash300

Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(d)

300

200

100

0

ndash100

ndash200

ndash300

Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(e)








11138681113868111386811138681113868

11138681113868111386811138681113868nminus c| _u|fp fp

11138681113868111386811138681113868

11138681113868111386811138681113868nminus1


11138681113868111386811138681113868

11138681113868111386811138681113868n

1113882 1113883 _u(5)






fbs kbsu (7)




+ c _u + λfp

(8)




k1 k10 He( 1113857 + k11 He( 1113857| _u| + k12 He( 1113857| _u|2 (9)

k3 k30 He( 1113857 + k31 He( 1113857| _u| (10)

c c0 He( 1113857 + c1 He( 1113857| _u| (11)

λ λ0 He( 1113857 + λ1 He( 1113857| _u| (12)



F1 fp1113872 1113873 uminus u+

F2 fp1113872 1113873 uminus u+







(13)


fp

αβ + c




minusαβ + c


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(14)



f

k1 + kbs( )u + k3u3 + c _u + λ

αβ + c




k1 + kbs( )u + k3u3 + c _u + λ

minusαβ + c


(15)



5 Conclusions




200

150

100

50

0

ndash50

ndash100

ndash150

ndash200

Dam

ping

forc

e (kN

)








Acknowledgments


References
























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls










Displacement (mm)

300250200150100

500


Dam

ping

forc

e (kN

)


01 Hz05 Hz10 Hz

15 Hz25 Hz



200

150

100

50

0

ndash50

ndash100

ndash150

ndash200

Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(a)

200250300

150100

500


Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(b)

200250300

150100

500


Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(c)

300

200

100

0

ndash100

ndash200

ndash300

Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(d)

300

200

100

0

ndash100

ndash200

ndash300

Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(e)








11138681113868111386811138681113868

11138681113868111386811138681113868nminus c| _u|fp fp

11138681113868111386811138681113868

11138681113868111386811138681113868nminus1


11138681113868111386811138681113868

11138681113868111386811138681113868n

1113882 1113883 _u(5)






fbs kbsu (7)




+ c _u + λfp

(8)




k1 k10 He( 1113857 + k11 He( 1113857| _u| + k12 He( 1113857| _u|2 (9)

k3 k30 He( 1113857 + k31 He( 1113857| _u| (10)

c c0 He( 1113857 + c1 He( 1113857| _u| (11)

λ λ0 He( 1113857 + λ1 He( 1113857| _u| (12)



F1 fp1113872 1113873 uminus u+

F2 fp1113872 1113873 uminus u+







(13)


fp

αβ + c




minusαβ + c


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(14)



f

k1 + kbs( )u + k3u3 + c _u + λ

αβ + c




k1 + kbs( )u + k3u3 + c _u + λ

minusαβ + c


(15)



5 Conclusions




200

150

100

50

0

ndash50

ndash100

ndash150

ndash200

Dam

ping

forc

e (kN

)








Acknowledgments


References
























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls




200

150

100

50

0

ndash50

ndash100

ndash150

ndash200

Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(a)

200250300

150100

500


Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(b)

200250300

150100

500


Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(c)

300

200

100

0

ndash100

ndash200

ndash300

Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(d)

300

200

100

0

ndash100

ndash200

ndash300

Dam

ping

forc

e (kN

)


0 A10 A

20 A30 A

(e)








11138681113868111386811138681113868

11138681113868111386811138681113868nminus c| _u|fp fp

11138681113868111386811138681113868

11138681113868111386811138681113868nminus1


11138681113868111386811138681113868

11138681113868111386811138681113868n

1113882 1113883 _u(5)






fbs kbsu (7)




+ c _u + λfp

(8)




k1 k10 He( 1113857 + k11 He( 1113857| _u| + k12 He( 1113857| _u|2 (9)

k3 k30 He( 1113857 + k31 He( 1113857| _u| (10)

c c0 He( 1113857 + c1 He( 1113857| _u| (11)

λ λ0 He( 1113857 + λ1 He( 1113857| _u| (12)



F1 fp1113872 1113873 uminus u+

F2 fp1113872 1113873 uminus u+







(13)


fp

αβ + c




minusαβ + c


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(14)



f

k1 + kbs( )u + k3u3 + c _u + λ

αβ + c




k1 + kbs( )u + k3u3 + c _u + λ

minusαβ + c


(15)



5 Conclusions




200

150

100

50

0

ndash50

ndash100

ndash150

ndash200

Dam

ping

forc

e (kN

)








Acknowledgments


References
























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls









11138681113868111386811138681113868

11138681113868111386811138681113868nminus c| _u|fp fp

11138681113868111386811138681113868

11138681113868111386811138681113868nminus1


11138681113868111386811138681113868

11138681113868111386811138681113868n

1113882 1113883 _u(5)






fbs kbsu (7)




+ c _u + λfp

(8)




k1 k10 He( 1113857 + k11 He( 1113857| _u| + k12 He( 1113857| _u|2 (9)

k3 k30 He( 1113857 + k31 He( 1113857| _u| (10)

c c0 He( 1113857 + c1 He( 1113857| _u| (11)

λ λ0 He( 1113857 + λ1 He( 1113857| _u| (12)



F1 fp1113872 1113873 uminus u+

F2 fp1113872 1113873 uminus u+







(13)


fp

αβ + c




minusαβ + c


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(14)



f

k1 + kbs( )u + k3u3 + c _u + λ

αβ + c




k1 + kbs( )u + k3u3 + c _u + λ

minusαβ + c


(15)



5 Conclusions




200

150

100

50

0

ndash50

ndash100

ndash150

ndash200

Dam

ping

forc

e (kN

)








Acknowledgments


References
























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls




f

k1 + kbs( )u + k3u3 + c _u + λ

αβ + c




k1 + kbs( )u + k3u3 + c _u + λ

minusαβ + c


(15)



5 Conclusions




200

150

100

50

0

ndash50

ndash100

ndash150

ndash200

Dam

ping

forc

e (kN

)








Acknowledgments


References
























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls






Acknowledgments


References
























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls






Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls




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The Mechanical Properties of a Novel STMR Damper Based on Magnetorheological Silly …downloads.hindawi.com/journals/amse/2018/2681461.pdf · 2019-07-30 · ResearchArticle The Mechanical