mr damping

Adaptive Tuned Vibration Absorber based onMagnetorheological Elastomer

H. X. DENG AND X. L. GONG*

CAS Key Laboratory of Mechanical Behavior and Design of MaterialsDepartment of Mechanics and Mechanical Engineering, University of Science and Technology of China

Hefei 230027, China

ABSTRACT: This study presents an adaptive tuned vibration absorber (ATVA) which isbased on magnetorheological elastomer (MRE). Traditional dynamic absorber has limited itsapplication and vibration absorption capacity for its narrow working frequency bandwidth.MRE is a kind of smart material whose modulus can be controlled by applied magnetic field.Based on MREs, an ATVA which works on shear mode is proposed in this study. Afterthe vibration mode shapes of the ATVA are analyzed, the mechanical structure of the ATVAis brought forward. Then the magnetic circuit of the ATVA is identified by ANSYS software.By using a modified dipole model, the shift-frequency properties of the ATVA versus magneticfield and strains are theoretically analyzed and simulated. Furthermore, by employing abeam with two ends supported, its shift-frequency property and vibration absorptioncapacity are experimentally justified. The experimental results demonstrate that the designedATVA has better performance than traditional passive absorber in terms of frequency-shiftproperty and vibration absorption capacity.

Key Words: magnetorheological elastomer, vibration absorber, semi-active.

INTRODUCTION

MOST of the mechanical, civil, and constructionsystems encounter undesirable vibrations. To

avoid damage, fatigue failure, and to increase thesystem lifetime, many researches have been done toattenuate the unwanted vibration. Dynamic vibrationabsorber (DVA) invented by Frahm (1909) is a classicsolution to suppress vibrations of machines andstructures. Traditional DVA is typically composed ofan oscillator, a spring element, and a damping element.However, this kind of passive absorber theoreticallybrings the object base to rest at a single excitationfrequency, the resonance frequency of the DVA. Formany practical systems, the working condition maychange over time and cause the absorber to becomeinefficient and potentially aggravate the base vibration.Adaptive tuned vibration absorber (ATVA) is developedto solve this problem, which is a device similar to DVAbut holds adaptive element to trace the workingcondition. Generally, ATVA can vary its naturalfrequency to track uncertain or time-varying excitationfrequencies by employing the adaptive spring elementwhich is able to alter its stiffness. According to the

method of changing the stiffness, the ATVAs canbe sorted into two major groups: one is to usevariable geometries (Walsh and Lamancusa, 1992;Li et al., 2005) and the other is to use smart materials(Flatau et al., 1998; Williams et al., 1999; Davis andLesieutre, 2000).

Magnetorheological elastomers (MREs) are smartmaterials where polarizable particles are suspended ina non-magnetic solid or gel-like matrix. Typically,magnetic fields are applied to the polymer compositeduring cross-linking so that chainlike structures can beformed and fixed in the matrix after curing. The uniquecharacteristic of MRE is that its shear modulus canbe controlled by the external magnetic field rapidly,continuously, and reversibly (Shen et al., 2004; Gonget al., 2005). Such properties make MREs promising inmany applications, such as ATVAs, stiffness tunablemounts and suspensions, and variable impedancesurfaces. Watson (1997) applied a patent using MREsfor a suspension bushing. Later, Stewart et al. (1998)and Ginder et al. (2000) constructed and tested tunableautomotive mounts and bushings based on MRelastomers. Ginder et al. (2001) did pioneer work onthe development of an adaptive tunable vibrationabsorber (ATVA) using MREs. Koo et al. (2003) atVirginia Tech University used magnetorheologicaldampers in semi-active tuned vibration absorbers to*Author to whom correspondence should be addressed.

E-mail: [email protected]

JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES, Vol. 18—December 2007 1205

1045-389X/07/12 1205–6 $10.00/0 DOI: 10.1177/1045389X07083128� SAGE Publications 2007

Los Angeles, London, New Delhi and Singapore © 2007 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution.

at University of Liverpool on March 14, 2008 http://jim.sagepub.comDownloaded from

http://jim.sagepub.com

control structural vibrations. Lerner and Cunefare(2007) examined MREs placed in three differentabsorber configurations: shear, longitudinal, andsqueeze modes and found the squeeze mode deviceexhibited the largest frequency shift of 507%.The objective of this study is to investigate the

application of MREs to adaptive tuned vibrationabsorber. The vibration mode shapes have beenanalyzed to ensure that the ATVA works by shearmode. Another problem to be confirmed is the magneticcircuit; a closed C-shape structure has been identified byANSYS software. Furthermore, the shift-frequencyproperties of the ATVA versus magnetic field andstrains are analyzed and simulated by using the modifiedmagnetic dipole model. It is also experimentally verifiedtogether with its attenuation ability.

MATERIAL PREPARATION

The MRE materials consist of natural rubber as amatrix, additives, and carbonyl iron particles with a size

of 3–5 m. At the first step of the fabricating process, allingredients are thoroughly mixed by mixing roll andthen the mixture is compressed into a mold and placedin a self-developed magnet-heat coupled device. Duringthe pre-cured stage, the particles are magnetized andform chains aligned along the magnetic field direction.Thirty minutes later, the magnetic field is turned offand the temperature is raised to 1538C to finish thesulfuration. The MRE properties under various mag-netic fields are evaluated by a modified dynamicmechanical analyzer (DMA) from the Triton Co. Itcan be seen from Figure 1 that the shear modulus showsan increasing trend with magnetic field intensity.However, the increasing slope decreases with theincrement of magnetic fields, which is due to themagnetic saturation. In addition, the magneto-inducedmodulus also shows an increasing trend with thedecreasing strain while the zero-field modulus is nearlythe same with the strain change.

DESIGN OF ATVA

Simulation of Mode Shapes

This study focuses on the ATVA which works byshear mode. So the first step of the design is toanalyze the vibration mode shape of the assumedATVA and make sure the work mode of ATVA isshear. To this end, ANSYS software is employed anda popular sandwich structure is simulated. In thisstructure, dynamic mass is at the center and throughMREs connecting the static mass. The results ofvibration mode shapes analyses are shown in Figure 2.Figure 2(a) shows that the first mode shape of ATVAis swing while Figure 2(b) shows the second mode isshear in plumb direction. It means that the sandwichstructure with this shape would easily swing instead ofshear. To avoid this happening, some structures tomake the ATVA work by shear mode should be

Figure 2. Mode shapes of sandwich structure.

1

1.5

2

2.5

3

3.5

Magnetic induction density (mT)

She

ar m

odul

us G

(M

Pa)

0.03%

0.17%

0.33%

0.5%

0.67%

100 200 300 400 500 600 700 800 900 10000

Figure 1. Shear modulus with magnetic field under differentstrains load.

1206 H. X. DENG AND X. L. GONG

© 2007 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution. at University of Liverpool on March 14, 2008 http://jim.sagepub.comDownloaded from


leaded in, such as guiderod, sliding chute, and linearbearing.

ATVA Structure

The efficient component for ATVA to absorb vibra-tion is its oscillator or dynamic mass. As shown inFigure 3, the developed ATVA consists of three mainparts: dynamic mass, static mass, and smart springelement with MREs. The electromagnets and magneticconductors form a closed C-shape magnetic circuit,which are assembled at the mounting shell. Thesecomponents together construct the dynamic mass. Thisdevelopment makes the ATVA more compact andmore efficient because no additional oscillator andnearly most components can be considered as dynamicmass. The static mass consists of the shear plate andthe base. Through the shear plate, the smart springelements (MREs) connect the dynamic mass and thestatic mass. Furthermore, as analyzed above, a guiderodand a linear bearing are employed to ensure the ATVAworks by the shear mode.

Magnetic Circuit Analyses

Magnetic conductor which forms a magnetic circuitwith MREs is the vital component of the ATVA basedon MREs. As shown in Figure 4, for shear mode, thedirection of magnetic field is parallel to the direction ofparticle chains while the shear force is perpendicularto the particle chains. The purpose of analyzing themagnetic circuit is to optimize the turn number of coils,the circuit, and the distribution of magnetic lines of flux,etc. The avail tool of the magnetic circuit analyses isANSYS software. Figure 5 is a result of the designedATVA. For a coil with 2200 rounds, when the appliedcurrent is 0.5A, the magnetic field through MRE canreach 0.9T, which is enough to utilize as shown inFigure 1.

THEORETICAL ANALYSIS OF

SHIFT-FREQUENCY PROPERTY

The MRE’s shear modulus G consists of twoterms, zero-field modulus G0 and magneto-inducedmodulus �Gd:

G ¼ G0 þ�Gd: ð1Þ

The natural frequency of the ATVA can beexpressed as:

f ¼ f0 þ�f ð2Þ

where f0 is the initial natural frequency and �f is themagneto-induced frequency:

f0 ¼1

2�

ffiffiffiffiffiffiffiffiffiG0A

mh

rð3Þ

�f ¼1

2�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiG0 � A

m� h

r�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ

�Gd

G0

r� 1

!: ð4Þ

From Equation (3), the initial resonant frequency of theATVA can be designed to match the primary system.Equation (4) reveals that the frequency-shift capacity isnot only related to the MR effect but also related to theinitial shear modulus. Large initial modulus withthe same MR effect will cause wide frequency-shiftbandwidth. To theoretically analyze the frequency-shiftproperty with magnetic field, a modified magneticdipoles model considering the interaction between allparticles at the same chain is employed. The model of asingle chain is shown in Figure 6, where d is the distance

Figure 5. The magnetic circuit of a C-shape structure.

1

9

8 6

7 5

2 3 4

Figure 3. The scheme of designed ATVA. 1. Cover; 2. Guiderod;3. Linear bearing; 4. Magnetic conductor; 5. Shear plate; 6. MREs;7. Base; 8. Electromagnet; 9. Mounting shell.

H

F

Figure 4. The directions of magnetic field and shear force.

Adaptive Tuned Vibration Absorber Based on MRE 1207



between two neighbor particles before deformation, and� is the shear angle. For small deformation,� ! 0, themagneto-induced modulus can be expressed as:

�G ¼ 3��m�0�2H2

0

R

d

� �3

�10

A2þ

2

B2

� �þ48��

A3

R

d

� �3 !

ð5Þ

where 3� is the effective susceptibility and it approaches3 for ferromagnetic particles, m0, mm correspond to thepermeability in vacuum and the relative one of thematrix respectively, ’ is the volume fraction ofparticles and R is the radius of the particle,A ¼ 1� 4� cos3 �ðR=dÞ3�, B ¼ 1þ 2� cos3 �ðR=dÞ3� and� ¼

P1

k¼1 1=k3 � 1:202. Defining the shear strain to be

", the magneto-induced modulus can be represented as:

�G ¼ 3��m�0�2H2

0

R

d

� �3

� �12a7ð1þ 2ba3 þ 14b2a6 � 8b3a9Þ

ð1� 4ba3Þ3ð1þ 2ba3Þ2

� �ð6Þ

where a ¼ ð1þ "2Þ�1=2, b ¼ ��ðR=dÞ3. Obtained fromEquation (5), Figure 7 shows that the natural frequencyof ATVA has increasing trend with magnetic field.In the initial stage, natural frequency acceleratesand then the rate of slope drives to stabilization

before saturation. From Equation (6), the influence ofshear strain to the shift-frequency property can beobtained and is shown in Figure 8 where the magneticfield is fixed as 800KA/m. The frequency decreaseswhile the strain increases and gets stabilized when shearstrain is 100%.

It can be seen that strain influences the shift-frequencyproperty so hugely that the amplitude of the ATVAmust be evaluated. The model of ATVA coupled withprimary system can be simplified as Figure 9, where m1

is the mass of primary system, k1 is the stiffness ofprimary system, !1 is the natural frequency of primarysystem, and x2 is the vibration amplitude of primarysystem, m2 is the mass of ATVA, k2 is the stiffnessof ATVA, !2 is the natural frequency of ATVA, andx2 is the vibration amplitude of ATVA. When externalexcitation is p1sin!t, the complex amplitude �x2 can be

140

130

120

110

100

90

80

70

60

500 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Nat

ural

freq

uenc

y (H

z)

Shear strain

Figure 8. Natural frequencies versus shear strain.

k1

k2 c2

m1

m2

x2

x1

ATVA

Primary system

Figure 9. Model of ATVA with primary system.

140

130

120

110

100

90

80

70

60

500 1 2 3 4 5 6 7 8

× 105H (A/m)

Nat

ural

freq

uenc

y (H

z)

Figure 7. Natural frequencies versus magnetic field.

H0d

i

i+1

i–1

q

Figure 6. The model of particle chain.




expressed as:

�x2 ¼p1ðk2 þ ic!Þ

�k22 þ ic!ðm1!21 � ðm1=m2Þk2 � k2ÞÞ

ð7Þ

The maximum shear displacement B2 is:

B2 ¼ �st þ jx2j ¼g

!2þ jx2j ð8Þ

where �st is the static deflection of ATVA. Figure 10 is aclassic example of calculated shear displacement withand without static deflection. The shear displacementwithout static deflection is relatively small comparedto the displacement with static deflection. It means thatthe static deflection has vast contribution to the sheardisplacement especially in the low frequencies. Solimiting the static deflection is a method to enhancethe tuned frequency band. It also can be seen that theshear displacement decreases sharply with the increasingexcitation frequency. When the excitation frequency ishigher than 40Hz in this example, the shear displace-ment trends to a stable level and has little influence ontuned frequency of ATVA. Thus, ATVA working withMRE should work at relatively high frequency band,because the stability of the shift-frequency propertywould have problems at low frequency band.

EXPERIMENTAL EVALUATION OF ATVA

Frequency-shift Property

To investigate the frequency-shift capability of theMREs a beam with both ends supported is employed.The developed ATVA is placed at the center of thebeam. White noise excitation applied to the beam isgenerated by an exciter. Two accelerometers are placedon the oscillator and the base beam to measure theirresponses, respectively. The measured signals are sent to

the dynamic signal analyzer. The transfer function canbe obtained by using FFT analysis and the testingresults are shown in Figure 11. It shows that the curvesof transfer function move rightward with the incrementof the magnetic field. The resonance frequency canbe obtained by reading the peak-to-peak value. It isshown in Figure 12. Its trend agrees well with thetheoretical results. The resonance frequency increasesfrom 41Hz at 0A to 63.75Hz at 0.6A and its relativefrequency change is as high as 155%.

Vibration Attenuation

Compared with the frequency-shift experiment, thedifference of system to evaluate vibration absorption isthat an impedance head is induced. The impedance headconnects with the beam and the exciter. The exciterprovides sinusoidal excitation to the beam with a linearfrequency scan. The base point impedance with variousmagnetic fields can be measured by the dynamic signalanalyzer. To evaluate the vibration absorption capacity,a ratio � of base point admittance HA with TVAand that Ho without TVA is employed to reflect theeffect of vibration absorption:

� ¼ 20 lg HA=HO

�� ð9Þ

0.12

0.1

0.08

0.06

0.04

0.02

0

0.12

0.1

0.08

0.06

0.04

0.02

010 20 30 40 50 60 70 80 90 100 10 20 30 40 50 60 70 80 90 100

Excitation frequency (Hz) Excitation frequency (Hz)

She

ar d

ispl

acem

ent (

m)

She

ar d

ispl

acem

ent (

m)with static deflection

m1=25 kgp1=1 kg

m2=5kgω1=60Hz

m1=25 kgp1=1 kg

m2=5kgω1=60Hz

with static deflection

Figure 10. The maximum shear displacement with and without static deflection.

0.25

0.2

0.15

0.1

0.05

00 10 20 30

Frequency (Hz)

B increase

40 50 60 70 80 90 100

Mag

nitu

de

Figure 11. The transfer function at various magnetic fields.

Adaptive Tuned Vibration Absorber Based on MRE 1209



The comparison of vibration absorption capacitybetween the ATVA and the passive DVA is shown inFigure 13. The upper data are the results of passiveDVA which is realized by fixing the current of ATVAand the lower data are the results of ATVA whosefrequency is tuned to trace the excitation frequency. Forthe passive DVA, the best vibration attenuationefficiency occurs at the natural frequency of the primarysystem. The effect becomes worse sharply while theexcitation frequency is apart from beam naturalfrequency and a new resonance hump occurs at 34Hz.For ATVA, in tunable frequency band, it has betterabsorbing effects than passive DVA.

CONCLUSIONS

In this study, a shear mode ATVA based on MREwas designed, simulated, and evaluated. After thevibration mode shapes of the ATVA are analyzed andthe magnetic circuit of the ATVA is identified by

ANSYS software, a compact and efficient ATVA isproposed. Furthermore, the shift-frequency propertiesof the ATVA versus magnetic field and strains areanalyzed and simulated by using the vibration theoryand the modified magnetic dipole model. It is alsoexperimentally verified together with its attenuationability. The experimental results demonstrate thatthe designed ATVA has better performance thantraditional passive absorber in terms of frequency-shiftproperty and vibration absorption capacity.

ACKNOWLEDGMENTS

Financial support from NSFC (Grant No. 10672154)and SRFDP of China (Project No. 20050358010) isgratefully acknowledged. Scholarship BRJH funding ofChinese Academy of Sciences is also appreciated.

REFERENCES

Davis, C.L. and Lesieutre, G.A. 2000. ‘‘An Actively Tuned Solid-StateVibration Absorber Using Capacitive Shunting of PiezoelectricStiffness,’’ Journal of Sound and Vibration, 232(3):601–617.

Flatau, A.B., Dapino, M.J. and Calkins, F.T. 1998. ‘‘High BandwidthTenability in a Smart Vibration Absorber,’’ Proceedings of SPIE,3327:463–473.

Frahm, H. 1909. ‘‘Device for Damping Vibrations of Bodies,’’US Patent, No. 989958.

Ginder, J.M. and Nichols, M.E., Elie, L.D. and Clark, S.M., 2000.‘‘Controllable-Stiffness Components Based on Magnetorheolo-gical Elastomers,’’ Proceedings of SPIE, 3985:418–425.

Ginder, J.M., Schlotter, W.F. and Nichols, M.E. 2001.‘‘Magnetorheological Elastomers in Tunable VibrationAbsorbers,’’ Proceedings of SPIE, 4331:103–110.

Gong, X.L., Zhang, X.Z. and Zhang, P.Q. 2005. ‘‘Fabrication andCharacterization of Isotropic Magnetorheological Elastomers,’’Polymer Testing, 24(5):669–676.

Koo, J.-H., Ahmadian, M. and Setareh, M. 2003. ‘‘ExperimentalEvaluation of Magnetorheological Dampers for Semi-activeTuned Vibration Absorbers,’’ Proceedings of SPIE, 5052:83–91.

Lerner, A.A. and Cunefare, K.A. ‘‘Performance of MRE-basedVibration Absorbers,’’ Journal of Intelligent MaterialSystems and Structures OnlineFirst, 05 May 2007 (doi:10.1177/1045389X07077850).

Li, J.F., Gong, X.L., Zhang, X.Z., Xu, Z.B. and Zhang, P.Q. 2005.‘‘The Research of Dynamic Properties of Adaptive TunedVibration Absorber,’’ Chinese Journal of ExperimentalMechanics, 20(4):507–514.

Shen, Y., Golnaraghi, M. F. and Heppler, G. R. 2004. ‘‘ExperimentalResearch and Modeling of Magnetorheological Elastomers,’’Journal of Intelligent Material Systems and Structures,15(1):27–35.

Stewart, W.M., Ginder, J.M., Elie, L.D. and Nichols, M.E. 1998.‘‘Method and Apparatus for Reducing Brake Shudder,’’US Patent, No.5,816,587.

Walsh, P.L. and Lamancusa, J.S. 1992. ‘‘A Variable StiffnessVibration Absorber for Minimization of Transient Vibrations,’’Journal of Sound and Vibration, 158(2):195–211.

Watson J.R. 1997. ‘‘Method and Apparatus for Varying the Stiffnessof a Suspension Bushing,’’ US Patent, No.5,609,353.

Williams, K.A., Chiu, G.T. and Bernhard, R.J. 1999. ‘‘Passive-adaptive Vibration Absorbers Using Shape Memory Alloys,’’Proceedings of SPIE, 3668:630–641.

20

10

0

−10

−20

−30

−4030 35

Adaptive TVA; Passive TVA

40 45 50 55 60 65

Frequency (Hz)

20lo

g (H

A/H

0)(d

B)

70 75 80

Figure 13. Comparison of vibration attenuation between ATVAand TVA.

70

65

60

55

50

45

40

35

300 0.1 0.2 0.3

Applied current (A)

Nat

ural

freq

uenc

y (H

z)

0.4 0.5 0.6

Figure 12. The relationship between applied current and resonancefrequency.




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