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A miniature MRE isolator for lateral vibration suppression of bridge monitoring equipment:

design and verification

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2017 Smart Mater. Struct. 26 047001

(http://iopscience.iop.org/0964-1726/26/4/047001)

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Technical Note

A miniature MRE isolator for lateral vibrationsuppression of bridge monitoringequipment: design and verification

Lujie Zhao1, Miao Yu1, Jie Fu1, Mi Zhu1 and Binshang Li2

1Key Lab for Optoelectronic Technology and Systems, Ministry of Education, College of OptoelectronicEngineering, Chongqing University, Chongqing 400044, People’s Republic of China2Anhui Weiwei Rubber Parts (Group) Co., Ltd, Anhui, Peopleʼs Republic of China

E-mail: yumiao@cqu.edu.cn

Received 14 November 2016, revised 11 January 2017Accepted for publication 1 February 2017Published 23 February 2017

AbstractThe testing accuracy and service life of long-span bridge monitoring equipment declines overtime due to the adverse effects of environmental vibration during its operation. Therefore, it isessential to use effective methods to reduce the vibration of these devices. In this paper, inspiredby the controllable and field-dependent properties of magnetorheological elastomer (MRE), aminiature laminated MRE isolator is designed and manufactured to provide a relatively stableworking environment for the monitoring equipment. The method and process of its specificdesign are elaborated in detail based on the shape factor, allowable seismic displacement, lateralstiffness, allowable vertical load and analysis of magnetic circuit. Besides, a series of dynamictests are conducted to obtain the characteristics of the MRE isolator under various loadingconditions. The experimental results show that the maximum increase of the effective stiffness is114.12% with the current increasing from 0 A to 3 A. Consequently, the validity of its design isconfirmed by a fuzzy control experiment.

Keywords: laminated MRE isolator, specific design, dynamic tests, effective stiffness, fuzzycontrol experiment

(Some figures may appear in colour only in the online journal)

1. Introduction

Continual monitoring of the physical state of bridges exposedto the adverse effects of environmental vibration can effec-tively prevent their sudden failure and in turn avoid serioushuman casualties and economic losses. Therefore, the detec-tion of the physical state of bridges has become an importanttechnology to ensure their safety. At present, large bridgeshave been installed with real-time monitoring systems [1, 2].These monitoring systems are composed of thousands ofsensors combined with corresponding controllers as shown infigure 1. Among them, some systems, such as the lasermeasurement system and fiber sensing system, require a strictexternal working environment [3–5]. However, bridges are

exposed to horizontal vibration induced by earthquakes, windvibration and vehicle–bridge coupling at a frequency below20 Hz [6, 7]. The existence of the horizontal vibration willaffect the accuracy and lifetime of these optical monitoringinstruments. For instance, the horizontal vibration of thebridge will cause the laser beam to move far away from thetarget, thereby reducing its testing accuracy. In order to solvethis problem, an isolating and energy dissipating device isinstalled between the bottom of the target and the top of thefoundation. Currently, the rubber isolator is a mature andeffective type of isolation equipment [8–10]. But, the char-acteristics of the rubber isolator are fixed due to the restric-tions of the material [11]. That is, once designed and installed,rubber isolation systems are quite effective in meeting design

Smart Materials and Structures

Smart Mater. Struct. 26 (2017) 047001 (16pp) https://doi.org/10.1088/1361-665X/aa5d97

0964-1726/17/047001+16$33.00 © 2017 IOP Publishing Ltd Printed in the UK1

goals but may be ineffective when the structure of aninstrument is changed or they are exposed to different types ofseismic waves.

In order to overcome the shortcomings of traditionalrubber isolators, several studies have proposed the concept ofsmart isolation systems whose stiffness or damping char-acteristics can vary with changes in the external environmentto achieve their optimal isolation effects [12–15]. Magne-torheological elastomer (MRE) [16–20], composed of poly-mer (e.g. rubber, etc) and the soft magnetic micron particles(e.g. carbonyl iron powder, etc) cured under an appliedmagnetic field, provides an option for the design of smartisolation systems. Simultaneously, the real-time changes inshear modulus and damping with the applied magnetic fieldprovide MRE with broad prospects for application in thevibration isolation area.

Much research has been done on MREs with many MREisolators designed with diverse structures applied in the fieldof vibration control and isolation. Opie et al [21] used roomtemperature vulcanizing (RTV) silicone rubber-based MREsto design and fabricate a vertical semi-active base isolator.The experiments on vibration control were carried out byutilizing the semi-active controller and the results illustratedthat compared with the passive cases, the attenuation of theresonance peak and load speed could reach 16% and 30%,respectively, under the controlled condition. Gong et al [22]designed a MRE isolator with a voice coil motor and used anon-off control strategy to test its performance. Experimentalresults displayed that the peak of the transfer rate was reducedby 70% under the controlled condition. Moreover, theattenuation of root-mean-square (RMS) and maximum loaddisplacement reached 36% and 50%, respectively. Behroozet al [23, 24] devised a semi-active/passive MRE isolationbearing based on rubbers and MREs. The control experimentof a three story building model was carried out by using aLyapunov-control strategy and an El Centro wave. Exper-imental results showed that the maximum acceleration anddisplacement at the top of the model could be reduced by 22%and 58%, respectively. Li et al [25, 26] designed a laterallaminated MRE bearing used in large scale building isolation,which consisted of multilayer thin MRE sheets bonded onto

multilayer thin steel plates. The experimental results revealedthat its lateral stiffness could be significantly changed underdifferent excitation currents and the maximum change was upto 1630%. This structure, which can ensure smaller horizontalstiffness, and at the same time, greatly improves its verticalbearing capacity, provides an alternative for MRE in the largebuilding isolation field. In addition, Yu et al [27] used thesame structure to design a laminated MRE bearing applied forseismic mitigation in bridge superstructures. The resonancefrequency of the integrated system could be tuned from 10 Hzto 20 Hz and this demonstrated its potential for seismicmitigation for bridge superstructures.

Research on MRE isolators has mainly been focused ontesting [21–30], modeling [24, 31–33] and control [21–23, 34, 35]. However, the specific design processes andprinciples of MRE are isolators rarely addressed. In thispaper, based on the requirements of vibration isolation foroptical monitoring instruments on bridges, a miniature MREisolator is designed and described in detail to provide designmethods for an engineering application of the MRE isolator.The basic size of the laminated MRE isolator is determined byfour important parameters and its internal magnetic field isdemonstrated by calculation and simulation. The rationality ofthe design is proven with the comparison of the theoreticaland test results. Furthermore, the effectiveness of the design isalso validated by the vibration control experiment and thesweeping-frequency test.

2. Design of laminated MRE isolator

2.1. Preparation and testing of MRE

In this work, a RTV silicon rubber (Type: SC-2110, BeijingSanchen Industrial New Material Co. Ltd, China) was chosenas the MRE matrix. Silicone oil was selected as the plasticizerand soft magnetic carbonyl iron particles (CIP, Type: JCF2-2,d=5∼8 μm, Jilin Nichkel Industry Co. Ltd, China) wereused as the filling particles. The mass fraction of CIP, RTVsilicon rubber and silicon oil is 70%, 15%, 15%, respectively.The CIP were added into the mixture of the RTV silicon

Figure 1. Safety monitoring system used for large bridges.

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Smart Mater. Struct. 26 (2017) 047001 Technical Note

rubber and silicone oil, and stirred vigorously for 25 min. Assoon as the viscosity of the reactant has obviously increased,the mixture was placed in a vacuum oven to remove the airbubbles and then packed into aluminum molds. Finally, aftercuring for 24 h under a constant magnetic field of 0.7 T alongthe thickness of the MRE, the samples that were 2 mm inthickness were completely prepared.

The dynamic mechanical properties of the MRE sampleswere investigated using an advanced rheometer (Type:MCR301, Anton Paar, Austria). The testing frequency was setto 6 Hz with the magnetic flux densities ranging from 0 T to0.85 T. It can clearly be seen that the shear storage modulusincreases non-linearly with increasing of the magnetic fluxdensities and decreases with increasing of the strain fromfigure 2(a). That means the magnetic field and strain have asignificant influence on the stiffness of MRE. Figure 2(b)presents the magnetorheological (MR) effect versus magneticflux density under various strains, where the maximum MReffect is 1100% with a strain of 0.1%, while it reduces to

180% with a strain of 20%. Hence, the test results indicatethat MRE is suitable for working under small strains and thischaracteristic is critical to the design of MRE isolators.

2.2. Structure of laminated MRE isolator

Figure 3 shows the isolation system consisting of four MREisolators used for the bridge monitoring equipment. Thebaseboards of the MRE isolators are fixed on the bridged-boxbottom and the bridge monitoring equipment is installed on asteel plate connected to the top plate of the MRE isolators. Inorder to be used in this system, the isolator must possess highvertical stiffness but low lateral stiffness, simultaneously. Thehigh vertical stiffness provides the isolator with the ability tocarry the upper gravity load, while the low lateral stiffness canoffer a lateral displacement to prevent the vibration frompassing on to the monitoring devices. Therefore, learningfrom traditional laminated rubber bearings, such as lead-corerubber bearings [36] and high damping rubber bearings [37],

Figure 2. Shear storage modulus and MR effect versus magnetic flux density under different strains for MRE: (a) shear storage moduluscurves and (b) MR effect curves.

Figure 3. Isolation system for the bridge monitoring equipment.

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Smart Mater. Struct. 26 (2017) 047001 Technical Note

a laminated structure where multilayer thin MRE sheets arebonded onto multilayer thin steel plates is adopted to design aMRE isolator for the experiment in this paper.

For the laminated MRE isolator, the design requirementsare determined by the upper target, material characteristicsand external environment. The working displacement of thelaminated MRE isolator is 2.5 mm for the micro-vibration ofthe environment. The safety monitoring system composed ofvarious monitoring instruments with different sizes andweights for large bridges is very complex. However, theweight of most optical monitoring instruments whose char-acteristics are high precision and low weight is not more than10 kg [3–5]. Therefore, the allowable vertical load of thelaminated MRE isolator is 2.5 kg and the total bearingcapacity of the isolation system 10 kg, as shown in figure 3,which is adequate for most of bridge optical monitoringinstruments. The maximum expected magnetic flux density inlaminated MRE sheets is 400 mT because the shear storagemodulus as shown in figure 2(a) tends to be saturated at400 mT, and a strong magnetic field requires high powerconsumption, which leads to heating phenomenon. Mostimportantly, the expected magnetic flux density must be largeenough for actual magnetic flux leakage in the MRE isolator[26]. Finally, due to the external vibration the natural fre-quency of the MRE isolator should be less than 20 Hz.

Four parameters are crucial to both theoretical evaluationand practical implementation for the performance of the

isolator, i.e. shape factor, allowable seismic displacement,lateral stiffness and allowable vertical load as part of thedesign process [29, 38]. The basic dimensions of the lami-nated MRE isolator can be ascertained according to the designrequirements and the four design parameters.

2.2.1. Shape factor. The MRE in the laminated bearing willhave lateral bulging phenomenon in the bearing process andthe shape factor is proposed to describe the phenomenon ofexpansion, which is given by [29, 38]:

( )pp

= = =SD

Dt

D

t

loaded area

force free area 4 41

2

Figure 4. Circular laminated MRE bearing under gravity and lateral loads.

Figure 5. The section-view of the new laminated MRE isolator.

Table 1. The dimensions of the laminated MRE isolator.

Parts Dimensions (mm)

Inner diameter of coil bobbin 38Diameter of under connecting plate 120Outer diameter of coil bobbin 70Thickness of coil bobbin 2Height of coil bobbin 37Inner diameter of steel sleeve 70External diameter of steel sleeve 76Height of steel sleeve 35Diameter of top cover and top connecting plate 120Height of whole apparatus 63

4

Smart Mater. Struct. 26 (2017) 047001 Technical Note

where D is the diameter of the MRE layers, and t is thicknessof a single layer cylindrical MRE (see figure 4). The choice ofshape factor has a great influence on the performance of thedevice. If the shape factor is too large, the shear stress of thelaminated MRE bearing will be reduced [39], and the MRElayers and steel plates will be easily stripped off [39].Consequently, the shape factor of the laminated MRE isolatoris determined to be 3.75 for isolation the vibration of smallequipment. The calculated result of the MRE’s thickness t is2 mm when the diameter of the MRE layers D is 30 mm.

2.2.2. Allowable seismic displacement. The effective workingdisplacement of laminated MRE isolator is limited by the smallMR effect under large strain. Therefore, appropriate workingdisplacement, allowable seismic displacement, is the key to thenormal operation of the isolator. The allowable seismicdisplacement of the laminated MRE isolator xd is given asfollows [29, 38]:

( )g=x h 2d w

where the maximum allowable shear strain gw is 20% in orderto ensure the effectiveness of the isolator for the low MR effectof MRE under large strain, and the effective height of MRElayers h is equal to 12.5 mm for xd is 2.5 mm. However, due tothe limit of the MRE’s thickness, the final effective height is12mm. Therefore, 6 layers of MREs with 2mm thicknesswhich are bonded to 5 layers of thin steel plates with 1mmthickness are used in the isolator and the overall height of thelaminated MREs with steel plates is 17 mm.

2.2.3. Lateral stiffness. The natural frequency of the isolator isdetermined by the lateral stiffness, which is lower than 20 Hz forthe limitation of the external vibration. The laminated structureof MREs and steel plates can severely limit the flexuraldeformations of the MRE isolator [24]. Consequently, it is

assumed that the isolator only has pure shear deformations andits lateral stiffness kbcan be approximated as [29, 38]:

( )p= =k

GA

h

GD

h43b

2

where G is the shear modulus of MRE, A is the area of MRElayers (full cross section area).

The relationship of the natural frequency f and the lateralstiffness kb can be described as:

( )p

=fk

m

1

24b

where m is the load of a single MRE isolator. From equations (3)and (4), the natural frequency is influenced by the weight ofinstruments, the cross-sectional area and the effective height ofMRE. The low natural frequency can be achieved by reducingthe cross-sectional area or increasing the thickness of the MRE.However, the vertical load will reduce if the cross-sectional areais too small, while the advantage of this multilayer structure willdisappear if the MRE is too thick. The maximum naturalfrequency of the laminated MRE isolator is 34.55 Hz with theexpected magnetic flux density of 400mT (the shear modulus ofthe MRE is 2MPa at 400mT with a strain of 0.1%), and itsminimum natural frequency is 6.08 Hz with the magnetic fluxdensity of 0mT (the shear storage modulus of the MRE is0.062MPa at 0mT with a strain of 20%).

2.2.4. Allowable vertical load. It is known that high verticalloading capacity is one of the main characteristics of the MREbearing for supporting the weight of targets. The allowablevertical load of the laminated MRE isolator can be written as[29, 38]:

( )g= ¢W A GS 5wmax

where ¢A is the overlap area from displaced top to bottom ofbearing (see in figure 4).

Based on equations (1) and (5), the allowable verticalload of the isolator is related to the modulus and strain of theMRE. So, it is estimated that the allowable vertical load of thelaminated MRE isolator is about 3.0 kg under the maximumallowable seismic displacement of 2.5 mm (20% strain) withno current applied to the isolator and it meets the designrequirements.

The structural design of the laminated MRE isolator islimited by many factors and the design parameters must beoptimized. Figure 5 shows a diagram of the structuralconfiguration of the laminated MRE isolator. It consists of sixlayers of MREs which are bonded onto five layers of thin steelplates. The laminated MRE sheets are placed in the center of an

Figure 6. Model of magnetic circuit for the laminated MRE isolator.

Table 2. The magnetic reluctance of the laminated MRE isolator.

Magneticcircuit

L1 L2 L3 L4 L5 Ltotal

Magneticreluctance(10^6H−1)

0.214 0.125 0.555 0.254 3.973 5.121

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Smart Mater. Struct. 26 (2017) 047001 Technical Note

electromagnetic coil with copper wires of 0.8mm in diameter,which can provide a uniform magnetic field when current passesthrough it. In order to ensure the safety of the isolator, thedistance between the laminated MRE sheets and coil bobbinmakes the MRE isolator have a maximum deformation of 4mm,which is bigger than the allowable seismic displacement.Moreover, there are two small grooves on the top cover andsteel sleeve with a depth of 1 mm, where 80 steel balls of2.8 mm in diameter are evenly distributed to prevent the upperand lower shaking of the top cover without changing the lateralstiffness of the MRE isolator as much as possible. In order tofacilitate the connection with the external device and reduce themagnetic leakage, a top connecting plate and a under connectingplate made of aluminum alloy are distributed on the top andbottom of the isolator, respectively. The final dimensions of theMRE isolator are listed in table 1.

2.3. Analysis of magnetic circuit

A magnetic field is the key to the MRE isolator workingproperly. So, it is worthwhile to study its magnetic field.Figure 6 shows a model of the magnetic circuit used for thelaminated MRE isolator. Kirchoff’s magnetic law can be usedto analyze the magnetic circuit design, which is given asfollows [28]:

( )å =H l NI 6i

n

i i

where Hi is the magnetic field intensity and li is the length ofthe ith magnetic flux path, N is the total winding number ofcoil and I is the excitation current.

In a weak magnetic field, the relationship betweenmagnetic flux density and magnetic field intensity can bewritten as:

( )m m=B H 7i i i0

where m p= ´ - H m4 1007 is the permeability of vacuum,

mi and Bi are the relative permeability and the magnetic fluxdensity for the ith magnetic flux path, respectively.

In addition, according to the Gauss theorem of magneticfield, the total magnetic flux passing through any closedsurface must be zero. For the laminated MRE isolator, eachsection forms a close loop. Therefore, the magnetic flux Fpassing through any part of the cross-sectional area Ai is thesame, which can be described as:

( )F = B A 8i i

Equations (6)–(8) can be simplified to:

( )å åm m= F ´ = F ´

= =

NIl

AL 9

i

ni

i i i

n

i1 0 1

wherem m

=Ll

Ai

i

i i0

is defined as the magnetic reluctance,

which can describe the blocking capacity of the flux. Theinfluence of magnetic reluctance to magnetic flux is the sameas the effect of resistance to current. Figure 6 shows the fivemain parts of magnetic reluctance, L1 to L .5 Therefore, usingthe function of magnetic reluctance, each part can be estab-lished as follows:

( )

( )

( )

ò

ò

m m p m m p m m p

m m p

m m p

m m p m m p

m m p m m p

= + +

=-

=-

=+

+

= +

Lh

r

h

r rhdr

Lh

r r

Lh

r r

Lh h

r rhdr

Lh

r

h

r

1

2

1

2

6 510

r

r

r

r

11

0 1 12

2

0 1 22

0 1 3

24

0 2 42

32

35

0 3 42

32

46 7

0 2 12

0 2 6

58

0 4 12

9

0 5 12

2

5

1

4

Figure 7. Electromagnetic simulation: (a) magnetic flux density and (b) magnetic flux path.

6

Smart Mater. Struct. 26 (2017) 047001 Technical Note

where =r 15 mm,1 =r 19 mm,2 =r 35 mm,3 =r 41 mm,4

=r 48 mm,5 =h 8 mm,1 = =h h 9 mm,2 7 =h 7 mm,3

=h 33 mm,4 = =h h 1 mm,5 9 =h 6 mm,6 =h 2 mm,8

m m= = 150,1 2 m = 1,3 m = 3.4,4 m = 16 0005 .

The calculation results are shown in table 2, wherethe magnetic reluctance of the laminated MRE sheets is thebiggest. Scilicet, MRE is the most important factor forthe magnetic field of isolator. Thence, the key to optimizethe magnetic circuit of isolator is to produce high-perme-ability MRE.

Based on equations (8)–(10), the magnetic flux density Bi

can be expressed as:

( )=BNI

A L11i

i total

Considering the limitation of the power dissipation andthe driver, the maximum excitation current is 3 A, and theexpected magnetic flux density in the laminated MREs is400 mT. Therefore, based on equation (11), the total windingnumber is about 500 turns.

Subsequently, in order to verify the correctness ofmagnetic circuit design and analyze the distribution of theinternal magnetic field, electromagnetic simulation of theMRE isolator is carried out using Ansoft Maxwell, which isused to calculate the electromagnetic properties under static,steady-state and transient conditions. The magnetic fluxdensity and magnetic flux path under the excitation current of3 A are shown in figure 7. The result indicates that the dis-tribution of magnetic field is uniform under the working areaof laminated MRE sheets. The design of the magnetic circuitis also proved to be correct by the magnetic flux density inlaminated MRE sheets of 420 mT, which is similar to thecalculation. Furthermore, in order to further understand thedistribution of the magnetic flux density inside the laminatedMRE sheets, figure 8(a) presents its distribution along thepath defined as A–B in figure 7(a) under different currents,

Figure 8. Magnetic flux density in the laminated MRE sheets: (a) path A–B, (b) path C–D.

Figure 9. The experimental setup of the MRE isolator.

Figure 10. Force response of the MRE isolator at 4 Hz and 6 mmwith different currents.

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Smart Mater. Struct. 26 (2017) 047001 Technical Note

Figure 11. The force-displacement relationships with displacement of 2.5 mm (1, 2, 4, 6 Hz).

Figure 12. The curve of effective stiffness of the MRE isolator versus currents.

8

Smart Mater. Struct. 26 (2017) 047001 Technical Note

and the distribution of the magnetic field is very uniform. Themagnetic flux density along the path C–D is shown infigure 8(b), where the magnetic flux density with both ends ofthe laminated MRE sheets is slightly larger than the middle ofthe magnetic field. In addition, the magnetic flux densitybetween the MRE sheets and the steel plates will be changedfor the different permeability of the two parts and its max-imum variation is about 10 mT.

3. Experimental testing and analysis

3.1. Dynamic mechanical properties of experimental setup

In order to evaluate the dynamic mechanical properties of thisMRE isolator, an experimental system shown in figure 9 wasbuilt. In the system, an electrodynamics vibration shaker(Type: DC-1000-15, Suzhou Sushi Testing Instrument Co.,Ltd, China) and a horizontal sliding table (Type: SV-0505,

Suzhou Sushi Testing Instrument Co., Ltd, China) were usedto provide sinusoidal excitation. The MRE isolator wasinstalled on the sliding table and moved along with it. A loadcell (BISE5110, No. 0748) was connected with the top coverby a fixed support so as to measure the lateral load generatedby the isolator. A laser displacement sensor (Type: SUNX-LM10, SUNX, Japan) was fixed to the ground in order todetect the displacement of the sliding table. The force anddisplacement signals were collected with a data acquisitioninstrument (Type: MDR-05, Beijing Aerostandard NewTechnology Company, China). During the experiment, a DCpower (Type: WYK-305B, EAST Electric Power SystemTechnology Co., Ltd, China) was employed to supply DCcurrent to the MRE isolator.

For all tests, various harmonic inputs with different dis-placements (0.5 mm, 1 mm, 2 mm and 2.5 mm equal to theshear strain of 4.2%, 8.3%, 16.7% and 20.8%) and differentfrequencies (1 Hz, 2 Hz, 4 Hz and 6 Hz) were chosen to test

Figure 13. The curve of effective stiffness of the MRE isolator versus loading frequency.

Figure 14. The curve of effective stiffness of the MRE isolator versus displacement.

9

Smart Mater. Struct. 26 (2017) 047001 Technical Note

the field-dependent properties of the MRE isolator with dif-ferent DC currents (0 A, 1 A, 2 A and 3 A).

3.2. Experimental results and analysis

The measurement of force-displacement is a very important tostudying viscoelastic materials (e.g. rubbers and MREs) anddevices and their characteristics. Figure 10 shows the forceresponse of the isolator at 4 Hz and 2.5 mm with differentcurrents, where the force increases with increasing current,10 N for 0 A and 18 N for 3 A. Figure 11 shows the force-displacement relationships under displacements of 2.5 mm,with different excitation frequencies and currents. From thefigure, one can see that the maximum force increases with theincrease in applied currents and magnitude of displacements.Since the slope and the enclosed area of the force-displace-ment loops represent the lateral stiffness and the equivalent

damping of the MRE isolator, respectively, it can also beobserved that both the lateral stiffness and the damping of theisolator increased significantly with the increasing currents.

3.2.1. Effective stiffness. The effective stiffness of the MREisolator, determined by the force-displacement loop, is givenas [26]:

( )=--

KF F

X X12d d

effmax min

max min

where Fd max is the force at the maximum displacement Xmax

of the loop and Fd min is the force at the minimumdisplacement Xmin of the loop.

Figure 12 presents the relations of its effective stiffnessversus the applied currents under various frequencies, whilethe loading amplitudes are 2 mm and 2.5 mm, respectively. It

Table 3. Effective stiffness (kN/m) of the isolator under different loading conditions.

Amplitude D=0.5 mm Amplitude D=1 mm

Frequency (Hz) Frequency (Hz)

Currents (A) 1 2 4 6 1 2 4 6

0 5.24 5.64 6.34 6.95 4.71 5.25 5.59 5.461 7.97 8.12 8.30 8.74 6.14 6.63 7.06 7.222 8.59 10.10 10.20 10.49 7.53 8.69 8.69 8.653 11.22 11.26 11.34 12.95 8.81 10.02 10.02 9.75Increasing (%) 114.12 99.64 78.86 96.51 87.05 70.67 79.25 78.57

Amplitude D=2 mm Amplitude D=2.5 mm

Frequency (Hz) Frequency (Hz)

Currents (A) 1 2 4 6 1 2 4 6

0 4.24 4.45 4.48 4.68 3.25 3.55 3.78 3.591 5.03 5.20 5.51 5.57 4.49 4.97 4.99 4.972 5.82 6.61 6.54 6.74 5.66 6.04 6.30 6.533 6.81 7.25 7.79 7.67 6.46 6.79 6.79 7.32Increasing (%) 60.61 62.92 73.88 63.89 98.77 91.27 91.27 103.9

Figure 15. The curve of equivalent damping versus currents.

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Smart Mater. Struct. 26 (2017) 047001 Technical Note

can be seen that the effective stiffness increases almostlinearly with applied currents and their variation trends almoststay the same under various frequencies. Moreover, theeffective stiffness increases with the increasing frequency, butthe increasing trend is not obvious. This phenomenon can beclearly observed in figure 13, where the variation of the

effective stiffness versus frequency is indicated, and thereason for this phenomenon is that the shear storage modulusof MRE changes little with the loading frequency. Figure 14shows the relationship between the effective stiffness and thedisplacement where the effective stiffness decreases withincreasing displacement, since the MR effect becomes smaller

Figure 16. The curve of equivalent damping versus loading frequency.

Table 4. Equivalent damping (Ns m−1) of the isolator under different loading conditions.

Amplitude D=0.5 mm Amplitude D=1 mm

Frequency (Hz) Frequency (Hz)

Currents (A) 1 2 4 6 1 2 4 6

0 34.8 33.6 31.7 15.4 61.3 38.5 46.5 42.51 272.5 155.8 31.5 26.3 187.2 79.9 66.8 58.72 367.7 87.3 60.5 41.2 278.0 130.6 81.9 74.83 454.1 182.9 115.4 66.2 359.5 162.3 104.0 72.8Increasing (%) 1205.5 445.1 263.8 329.0 486.6 321.4 123.9 71.1

Amplitude D=2 mm Amplitude D=2.5 mm

Frequency (Hz) Frequency (Hz)

Currents (A) 1 2 4 6 1 2 4 6

0 96.1 72.5 53.7 35.6 191.9 99.9 56.5 38.51 159.5 103.1 62.4 41.8 243.6 119.2 63.6 47.72 238.5 138.0 82.0 60.7 291.9 149.0 79.3 54.73 318.3 173.1 94.7 67.2 336.7 178.8 96.3 56.2Increasing (%) 231.1 138.8 76.3 89.0 75.4 79.0 70.5 46.0

Table 5. Comparison of the effective stiffness (kN/m) between theoretical and experimental data.

4% shear strain 20% shear strain

Current (A) Theoretical stiffness Experimental stiffness Error (%) Theoretical stiffness Experimental stiffness Error (%)

0 6.62 6.95 4.75 3.64 3.59 −1.391 14.07 8.74 −60.98 5.46 4.97 −9.862 19.73 10.49 −88.08 6.96 6.53 −6.583 25.34 12.95 −95.67 7.87 7.32 −7.51

11

Smart Mater. Struct. 26 (2017) 047001 Technical Note

under larger strain as shown in figure 2(b). For a givenloading frequency and a current, its relative decrease isaround 40% with the displacement increasing from 0.5 mmto 2.5 mm.

Table 3 lists all of the effective stiffnesses under differentloading conditions, where the maximum increasing of theeffective stiffness is 114.12% as the current increases from0 A to 3 A. Compared with different loading conditions, theeffective stiffness of the MRE isolator is mainly affected bythe currents and the loading displacements. Under largestrain, the decrease of the MR effect is one of the mostimportant factors limiting the application of MRE in theengineering field.

3.2.2. Equivalent damping. For characterizing the energy-dissipation performance of the MRE isolator, equivalentdamping is adopted, described as [26]:

( )p

=CEDC

fX213eq 2 2

where EDC is the area of each force-displacement loop, f isthe loading frequency and X is the maximum loadingdisplacement.

Figures 15 and 16 show that the equivalent damping of theMRE isolator increases linearly with the increasing appliedcurrent, but decreases exponentially with the increasing loadingfrequency under the displacements of 2 mm and 2.5mm. Inaddition, the lower the frequency of excitation, the more obviousthe variation of the equivalent damping with the current, whilethe greater the applied current, the more significant the changingof the equivalent damping with the frequency. All the dampingresults are listed in table 4 and its maximum increasing is1205.5% as the current increases from 0A to 3A when theloading frequency is 1 Hz and displacement is 0.5mm.

Figure 17. Photo of the experimental setup: (a) the MRE isolationsystem and (b) the MRE isolation platform.

Figure 18. The magnitude and phase-frequency curves of transmissibility under different currents: (a) the magnitude-frequency curve and (b)the phase-frequency curve.

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Smart Mater. Struct. 26 (2017) 047001 Technical Note

Moreover, the increasing of the equivalent damping attenuatesdistinctly with the larger displacement. So, it can be concludedthat the variation of damping is related to the current, thedisplacement and the frequency through analyzing these data.

The natural frequency of the MRE isolator is directlyrelated to its lateral stiffness, which is affected by theexcitation current and the amplitude of the external excitation.The theoretical stiffness of the MRE isolator can be calculatedaccording to the shear storage modulus of the MRE andequation (3). However, the actual stiffness of the MREisolator is far less than its theoretical frequency due to theexistence of serious magnetic flux leakage. Table 5 shows thecomparison of the effective stiffness between theoretical andexperimental data. It is obvious that the theoretical value isbasically consistent with the experimental value with 0 A,while the error increases with the increasing current and themaximum error can reach −95.67%. In addition, under thecondition of large strain (20% shear strain), there is littledifference between the experimental value and the theoreticalvalue. In the design process of the MRE isolator, there are alot of differences between the actual results and the theoreticalgoals for the magnetic flux leakage [26]. Therefore, the effectof magnetic flux leakage must be considered in the early stage

of the MRE isolator’s design and the design margin of themagnetic field should be enlarged to ensure that theperformance meets the requirements.

3.3. Transmissibility and phase responses of the isolationsystem

The results of the dynamic mechanical properties show thatthe MRE isolator possesses good magnetic-control char-acteristics. In this section, the transmissibility of the isolationsystem shown in figure 3 is tested and discussed.

Figure 17 shows the experimental setup to evaluate thetransmissibility of the isolation system. In the testing system,four identical MRE isolators are installed on a horizontalsliding table and the isolated target is installed on a steel plateconnected to their top plates. An electromagnetic exciter(Model JZK-50, Sinocera Piezotronics, China) is connectedwith the sliding table and driven by a sine sweeping-fre-quency waveform produced by a signal generator (Model33120 A, Agilent, USA) and amplified by a power amplifier(Model YE5874, Sinocera Piezotronics, China). Two accel-erators (Model 333B52, Piezotronics, USA) are arranged onthe surface of the sliding table and the steel plate to measurethe excitation and response signals, respectively. A dataacquisition instrument (Model MDR-05, Beijing Aero-standard New Technology Company, China) is used to collectacceleration signals and send them to a computer. Meanwhile,four DC powers (Model WYK-305B, EAST Electric PowerSystem Technology Co., Ltd, China) supply currents for theseMRE isolators.

The frequency of the sine sweeping-frequency excitationis changed from 5 Hz to 20 Hz and the value of its accel-eration peak is 0.1 g, while the DC currents are independentlyaltered from 0 A to 3 A with 1 A increments. The total weightof the steel plate and the laser is 6.75 kg.

Figure 18 displays the magnitude and phase-frequencycurves of transmissibility under different currents. It isobvious that the resonance frequency of the isolation systemincreases with the increase of input currents. This system canbe represented by the Kelvin model [27, 34]. The parameters,such as stiffness and damping, are identified in figure 18(a)and the formulas in [27]. Table 6 provides the parameters ofthe MRE isolation system, where the resonance frequency isincreased by 70.09% with the input currents increasing from0 A to 3 A. Moreover, the stiffness and the damping of thesystem are increased by 198.74% and 130.44%, respectively.

Table 6. The parameters of the MRE isolation system.

Input currents

Parameters 0 1 2 3 Increase (0A–3 A)

Resonance frequency (Hz) 9.26 10.85 12.86 15.75 70.09%Stiffness (kN m−1) 23.81 32.98 46.84 71.13 198.74%Damping (Ns m−1) 113.06 147.20 193.43 260.54 130.44%

Figure 19. Experimental setup of the vibration control system for theisolation system.

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Smart Mater. Struct. 26 (2017) 047001 Technical Note

Ultimately, the result of the sweep-frequency test illus-trates that the resonance frequency of the isolation system iswithin 20 Hz when the input currents are changed, and it isconsistent with the design requirements.

3.4. Experimental validation of the isolation system with a fuzzycontroller

In order to further verify the effectiveness of the isolationsystem for the bridge monitoring equipment, a vibrationcontrol system shown in figure 19 with a fuzzy controller isset up. In the system, the signal generator, the poweramplifier and the electromagnetic exciter are used to

generate sine excitation. The excitation and response signalsmeasured by the two accelerometers are sent to the dSPACEAutoBox (Model ds1005, dSPACE, Germany), where thefuzzy controller is downloaded. Four current drivers convertthe control voltage output by the controller to the controlcurrent to drive the four MRE isolators, and the DC powerssupply constant voltage for these drivers. The concretedesign of the fuzzy controller and the control principle aredescribed fully in [34].

Over the course of the experiment, a sine single-fre-quency excitation is produced by the electromagnetic exciterand its peak values of acceleration are 1 m s−2. The fre-quencies are also chosen from 8–17 Hz in 1 Hz increments.

Figure 20. Experimental results with a fuzzy controller and 8 Hz excitation: (a) the acceleration response, (b) the control current.

Figure 21. Experimental results with a fuzzy controller and 14 Hz excitation: (a) the acceleration response, (b) the control current.

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Smart Mater. Struct. 26 (2017) 047001 Technical Note

Figure 20 indicates the acceleration response and thecontrol current of the isolation system with the sine excitationof 8 Hz. The RMS of the fuzzy-off response acceleration is0.8933 m s−2, while the fuzzy-on response acceleration is0.8204 m s−2, which is reduced by 8.16%. Figure 21 gives theacceleration response and the control current of the isolationsystem with the sine excitation of 14 Hz. The RMS values ofthe fuzzy-off and the fuzzy-on are 1.6971 m s−2 and1.4470 m s−2, respectively, and the attenuation of the RMS is14.73% after fuzzy control.

Figure 22 presents the frequency response of the isolationsystem with sinusoid base excitations. The transmissibilitywith fuzzy control has obvious attenuation, compared with nofuzzy control, and the maximum attenuation is 18.31% withthe frequency of 12 Hz. Therefore, the vibration controlexperiment verifies the effectiveness of the isolation systemfor the bridge monitoring equipment.

4. Conclusion

A detailed design method based on a lateral laminated MREisolator is proposed in this paper. The design of the structureand magnetic circuit was carried out to ensure the shapefactor, allowable seismic displacement, allowable verticalload, lateral stiffness and distribution of magnetic field. Thebehaviors of the MRE isolator were experimentally tested andresults were analyzed based on two important measures, i.e.effective stiffness and equivalent damping. Its maximumincreasing of the effective stiffness is 114.12% as the currentincreases from 0 A to 3 A, and the isolator can be used as acontrollable stiffness device. Moreover, the rationality of thedesign is also verified by the fuzzy control experiment.Consequently, following the analysis mentioned above, thelaminated MRE isolator has great potential in the field ofvibration suppression for bridge monitoring equipment andthis design approach is valuable for the MRE isolator.

Acknowledgments

This research is funded by Chongqing Research Program ofBasic Research and Frontier Technology (Grant No.CSTC2015JCYBX0069), the Fundamental Research Fundsfor the Central Universities (Grant No. CDJXY120004) andthe Natural Science Foundation of Chongqing (Grant No.CSTC201JCYJA0848). The authors are grateful for theirsupport.

References

[1] Lynch J P et al 2006 Performance monitoring of theGeumdang Bridge using a dense network of high-resolutionwireless sensors Smart Mater. Struct. 15 1561–75

[2] Jang S et al 2010 Structural health monitoring of a cable-stayedbridge using smart sensor technology: deployment andevaluation Smart Mater. Struct. 6 439–59

[3] Costa B J A and Figueiras J A 2012 Fiber optic basedmonitoring system applied to a centenary metallic archbridge: design and installation Eng. Struct. 44 271–80

[4] Chan T H T et al 2006 Fiber Bragg grating sensors forstructural health monitoring of Tsing Ma bridge: backgroundand experimental observation Eng. Struct. 28 648–59

[5] Maaskant R et al 1997 Fiber-optic Bragg grating sensors forbridge monitoring Cement Concrete Comp. 19 21–33

[6] Ashkenazi V and Roberts G W 1997 Experimental monitoringof the Humber Bridge using GPS P. I. Civil Eng.-Civ. En.120 177–82

[7] Erdogan H, Akpinar B, Guelal E et al 2007 Monitoring thedynamic behaviors of the Bosporus Bridge by GPS duringEurasia Marathon Nonlinear Proc. Geoph. 14 513–23

[8] Kelly J M 1986 A seismic base isolation: review andbibliography Soil Dyn. Earthq. Eng. 5 202–16

[9] Sjöberg M and Kari L 2003 Testing of nonlinear interactioneffects of sinusoidal and noise excitation on rubber isolatorstiffness Polym. Test. 22 343–51

[10] Tsang H H 2008 Seismic isolation by rubber–soil mixtures fordeveloping countries Earthq. Eng. Struct. D 37 283–303

[11] Tyler R G 1991 Rubber bearings in base-isolatedstructures―a summary paper Bulletin of the New ZealandNational Society for Earthquake Engineering 24 251–74

[12] Spencer B F, Johnson E A and Ramallo J C 2000 ‘Smart’isolation for seismic control JSME Int. J. C-Mech. Sy. 43704–11

[13] Ramallo J C, Johnson E A and Spencer B F 2002 ‘Smart’ baseisolation systems J. Eng. Mech. 128 1088–99

[14] Yoshioka H, Ramallo J C and Spencer B F 2002 ‘Smart’ baseisolation strategies employing magnetorheological dampersJ. Eng. Mech. 128 540–51

[15] Koo J H et al 2009 A feasibility study on smart base isolationsystems using magneto-rheological elastomers Struct. Eng.Mech. 32 755–70

[16] Fuchs A et al 2007 Development and characterization ofmagnetorheological elastomers J. Appl. Polym. Sci. 1052497–508

[17] Popp K M et al 2010 MRE properties under shear and squeezemodes and applications J. Intel. Mat. Syst. Str. 21 1471–7

[18] Qi S et al 2016 Creep and recovery behaviors ofmagnetorheological elastomer based on polyurethane/epoxyresin IPNs matrix Smart Mater. Struct. 25 015020

[19] Yu M et al 2015 A dimorphic magnetorheological elastomerincorporated with Fe nano-flakes modified carbonyl ironparticles: preparation and characterization Smart Mater.Struct. 24 115021

Figure 22. Frequency response to sinusoid base excitations.

15

Smart Mater. Struct. 26 (2017) 047001 Technical Note

[20] Yu M et al 2015 A high-damping magnetorheologicalelastomer with bi-directional magnetic-control modulus forpotential application in seismology Appl. Phys. Lett. 107111901

[21] Opie S and Yim W 2011 Design and control of a real-timevariable modulus vibration isolator J. Intel. Mat. Syst. Str. 22113–25

[22] Liao G J et al 2012 Development of a real-time tunable stiffnessand damping vibration isolator based on magnetorheologicalelastomer J. Intel. Mat. Syst. Str. 23 25–33

[23] Behrooz M, Wang X and Gordaninejad F 2014 Performance ofa new magnetorheological elastomer isolation system SmartMater. Struct. 23 045014

[24] Behrooz M, Wang X and Gordaninejad F 2014 Modeling of anew semi-active/passive magnetorheological elastomerisolator Smart Mater. Struct. 23 045013

[25] Li Y C et al 2013 A highly adjustable magnetorheologicalelastomer base isolator for applications of real-time adaptivecontrol Smart Mater. Struct. 22 095020

[26] Li Y C et al 2013 Development and characterization of amagnetorheological elastomer based adaptive seismicisolator Smart Mater. Struct. 22 035005

[27] Xing Z W et al 2015 A laminated magnetorheologicalelastomer bearing prototype for seismic mitigation of bridgesuperstructures J. Intel. Mat. Syst. Str. 26 1818–25

[28] Xing Z W et al 2016 A hybrid magnetorheological elastomer-fluid (MRE-F) isolation mount: development andexperimental validation Smart Mater. Struct. 25 015026

[29] Li Y C, Li J C and Li W H 2013 Design and experimentaltesting of an adaptive magneto-rheological elastomer base

isolator The 2013 IEEE/ASME Int. Conf. on AdvancedIntelligent Mechatronics, pp 381–6

[30] Yang J et al 2014 A novel magnetorheological elastomerisolator with negative changing stiffness for vibrationreduction Smart Mater. Struct. 23 105023

[31] Li Y C and Li J C 2015 A highly adjustable base isolatorutilizing magnetorheological elastomer: experimental testingand modeling J. Vib. Acoust. 137 011009

[32] Yu Y et al 2016 A hysteresis model for dynamic behaviour ofmagnetorheological elastomer base isolator Smart Mater.Struct. 25 055029

[33] Yang J et al 2013 Experimental study and modeling of a novelmagnetorheological elastomer isolator Smart Mater. Struct.22 117001

[34] Fu J et al 2016 Model-free fuzzy control of a magnetorheologicalelastomer vibration isolation system: analysis andexperimental evaluation Smart Mater. Struct. 25 035030

[35] Yang J et al 2016 Development of a novel multi-layer MREisolator for suppression of building vibrations under seismicevents Mech. Syst. Signal Pr 70 811–20

[36] Robinson W H 1982 Lead-rubber hysteretic bearings suitablefor protecting structures during earthquakes Earthq. Eng.Struct. D 10 593–604

[37] Fuller K N G et al 1997 High damping natural rubber seismicisolators J. Struct. Contr. 4 19–40

[38] Filiatrault A 2013 Elements of Earthquake Engineering andStructural Dynamics 3rd edn (Montreal: PolytechnicInternational) pp 376–90

[39] Gent A N and Lindley P B 1959 The compression of bondedrubber blocks Proc. Instn. Mech. Engrs. 173 111–22

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