Numerical modeling of magnetoelectric effect in a composite structureY. X. Liu, J. G. Wan, J.-M. Liu, and C. W. Nan

Citation: Journal of Applied Physics 94, 5111 (2003); doi: 10.1063/1.1610806 View online: http://dx.doi.org/10.1063/1.1610806 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/94/8?ver=pdfcov Published by the AIP Publishing Articles you may be interested in The effects of interface misfit strain and surface tension on magnetoelectric effects in layered magnetostrictive-piezoelectric composites J. Appl. Phys. 114, 044109 (2013); 10.1063/1.4816693 Piezoelectric single crystal langatate and ferromagnetic composites: Studies on low-frequency and resonancemagnetoelectric effects Appl. Phys. Lett. 100, 052901 (2012); 10.1063/1.3679661 Effect of inclusion deformation on the magnetoelectric effect of particulate magnetostrictive/piezoelectriccomposites J. Appl. Phys. 102, 063908 (2007); 10.1063/1.2781513 Magnetoelectric properties of multiferroic composites with pseudo-1-3-type structure J. Appl. Phys. 99, 124108 (2006); 10.1063/1.2208734 Enhanced magnetoelectric effect in core-shell particulate composites J. Appl. Phys. 99, 08J503 (2006); 10.1063/1.2165147

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JOURNAL OF APPLIED PHYSICS VOLUME 94, NUMBER 8 15 OCTOBER 2003

[This a

Numerical modeling of magnetoelectric effect in a composite structureY. X. LiuLaboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, People’s Republic of Chinaand Department of Civil Engineering, Logistical Engineering University, Chongqing, People’s Republicof China

J. G. WanLaboratory of Solid State Microstructure, Nanjing University, Nanjing 210093, People’s Republic of China

J.-M. Liua)

Laboratory of Solid State Microstructure, Nanjing University, Nanjing 210093, People’s Republic of Chinaand International Center for Materials Physics, Chinese Academy of Sciences, Shenyang, People’sRepublic of China

C. W. NanDepartment of Materials Science and Engineering, Tsinghua University, Beijing, People’s Republic of China

~Received 3 February 2003; accepted 28 July 2003!

The mechanical coupling effect in a magnetoelectric~ME! composite structure in which amagnetostrictive component is bonded with a piezoelectric one is simulated by numerical technique,focusing on an optimization of the magnetoelectric coupling output. The simulation starts from anexperimentally developed ME composite structure and takes into account the mechanical couplingmechanism between the two components. A numerical optimization algorithm is developed,predicting a significant enhancement of the ME output by optimizing the component dimension.This algorithm can also be used for optimum design of other ME composite structures in terms ofthe largest ME output. ©2003 American Institute of Physics.@DOI: 10.1063/1.1610806#

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I. INTRODUCTION

Magnetoelectric~ME! effect is a cross two-field effectcharacterized by appearance of an electric polarizatioPupon applying a magnetic fieldH or with the change ofmagnetizationM on applying an electric fieldE.1–3 As apotential magnetic field probe and transducer for magnelectric conversion among many other applications, theeffect has been attracting attention since its discovery hcentury ago.4 Besides the ferroelectromagnets as the lotime objects of the related researches, ME-composite mrials represent the systems where strong ME effectpredicted based on the idea of product property of compomaterials.5 The ME composite consists of a magnetostrictcomponent combined with a piezoelectric component imacro- or micromixing form, where the ME effect is acvated by the mechanical coupling between the two typefunctional components, which can be mapped as:1

Magnetoelectric5electrical

mechanical3

mechanical

magnetic. ~1!

Along this line, quite a number of ME composite materiawere fabricated in order to reach the optimized ME effeFor example, Van den Boomgaadet al.6,7 synthesized a bulkcomposite of CoFe2O4 ~CFO! and BaTiO3 , although the ex-perimental ME yield was only about 1%–2% of the theorical prediction. The CFO-PZT@Pb(Zr0.52Ti0.48)O3# multilay-ered structures prepared by Harsheet al.8 show a ME-voltage coefficientaE of ;75 mV/cm Oe, also much lowe

a!Author to whom correspondence should be addressed; electronicliujm@nju.edu.cn

51110021-8979/2003/94(8)/5111/7/$20.00

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than the predicted value. TheaE for a NFO ~nickel ferrite!/PZT multilayered structure prepared using the tape castechnique was;1500 mV/cm Oe.9,10 The giant ME effect(aE;5900 mV/cm Oe) was measured in a sandwiched coposite structure stacked alternatively by large magnetostive material Tb0.3Dy0.7Fe1.9 ~Terfenol-D! and PZT disks,11,12

while the theoretical estimation still gives a higheraE value.The great difference between the experimental data

theoretical prediction reminds us of the necessity of rescale modeling of the ME effect in those ME composite mterials. One may argue that the mechanical coupling betwthe two components is highly structure sensitive. Furthmore, the mechanical resonance to be realized, which icourse component-dimension sensitive, is essential for hME output, while an experimental search for such a renance is tedious and costive. On the other hand, a numemodel of the ME effect is definitely suggestive for predesiand optimization of ME composite materials and structuof potential giant ME property.

In this article, we focus on the numerical modelingthe giant ME effect in a ME composite structure which cosists of Terfenol-D/epoxy composite@magnetostrictive com-ponent~MSCP!# bonded with PZT/epoxy composite@piezo-electric component~PECP!#. This ME composite structurewas recently developed by the authors and a giant ME efwas recorded at the resonance mode.13 It will be shown thatthe numerical algorithm to be developed here can reprodwell the experimental results. More importantly, the optimzation by the numerical algorithm allows us to argue thaslight adjustment of the component dimensions can enhasignificantly the ME output.il:

© 2003 American Institute of Physics

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II. MAGNETOELECTRIC COUPLING MODEL ANDNUMERICAL PROCEDURE

The ME composite structure in our earlier experimeoperates on the longitudinal vibration mode and a strongyield at the resonance frequency was observed. The strucis schematically illustrated in Fig. 1, where the arrowsM andP show the poling direction of PECP and magnetic domorientation of MSCP, respectively. The details of the strture fabrication and measurement of the ME effect wasscribed in our previous report.13 The roughly optimized di-mensions (L5 length, W5width, and T5thickness,unit:mm! of the two components areL57, W56.6, andT51.0 for MSCP, andL513.3, W56.6, and T51.0 forPECP. The magnetic field was applied along direction ofMand a displacement in MSCP was generated by the matostrictive effect that was transferred to the bonded PEThe transverse piezoelectric effect leads to the voltagetween the top and bottom surfaces in PECP. Furthermorwas revealed that by applying a magnetic bias of 0.7 kthe peak intensity ofaE at resonance frequency reaches up;8700 mV/cm Oe. The frequency dependence and magnbias dependence ofaE were measured too. Our numericsimulations suggest that a higher conversion efficiency tthe measured one can be achieved if the coupling paramesuch as the dimensions of MSCP and PECP and thenresonance frequency are optimized.

The numerical modeling of the ME coupling in our Mcomposite structure was performed by employing the finelement-analysis based on theANSYS Finite Element soft-ware. The experimental results can be well reproducedour numerical analysis. To take into account the mechanmechanism of the structure, a physically reasonable optimprocedure will be proposed. It is predicted from this procdure that the experimentally developed structure can betimized in terms of the enhanced coupling effect.

The numerical simulation of the ME effect is basedthe linear constitutive relations for MSCP and PECP mping the magnetostrictive and piezoelectric effects, resptively. The constitutive relation for MSCP can be written a

s5CH«2dH, ~2!

B5dT«1m«H, ~3!

FIG. 1. Schematic illustration of the ME structure.

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wheres and« denote the stress and strain in MSCP,B andHare the magnetic flux and magnetic field strength, whileCH,d, and m« are the elastic stiffness constants at a fixedH,magnetostrictive coupling coefficients and magnetic permability at constant strain, respectively.

For Terfernol-D, the three coefficients (CH, d, andm«)are more or less dependent on the magnetic and stress fii.e., the magnetomechanical interaction is a nonlinear cpling effect.14–16 The nonlinear harmonic response analyof the ME coupling in our ME composite structure remaichallenging since it requires huge computation capacity,the convergence of computation would be suspicious in socases. A linear simplifying procedure would avoid these ostacles without sacrificing the physics reliability. Convetionally, in order to obtain large intensity ofaE , a dc mag-netic bias should be applied on the magnetostrictcomponent. Compared to the value of this dc magnetic bthe amplitude of the applied ac magnetic field is very smAmong this small range of magnetic field, the three coecients (CH, d, andm«) could be regarded as constants, adetermined as the secant modulus of the correspondinglinear curves. Here, the determination of magnetostrictcoupling coefficient,d, is taken as an example. The depedence of induced stresss on H is schematically shown inFig. 2. Denote the value of dc magnetic bias byH0 , theamplitude of ac magnetic field byDH, and the corresponding increment of induced stress byDs, one has the couplingcoefficientd:

d5Ds/DH, ~4!

From Fig. 2, one sees that a largeaE corresponds to a larged. At the steepest point of theH-s curve, the variation oftangent modulus is relatively small, and could be replacedthe secant modulus. The corresponding dc magnetic bH0 , is the optimized magnetic bias. The computations in tarticle refer to the case of the optimized magnetic bias. Tcomparison between the calculation and experimental reswould show that this simplification is reasonable.

The constitutive relation for PECP can be written as:

s5CE«2eE, ~5!

D5eT«1l«E, ~6!

FIG. 2. Schematic illustration of determination of magnetostrictive couplcoefficients of MSCP.

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wheres and« denote the stress and strain in PECP,D, andEare the electric displacement and electric field,CE, e, andl«

are the elastic stiffness constants at a fixedE, piezoelectriccoefficients and dielectric constants at constant strain,spectively.

The behavior of MSCP could not be computed direcby ANSYS5.5/Multiphysics. As an approximation, MSCPsubstituted by PECP, noting the fact that the constitutequations of MSCP@Eqs. ~2! and ~3!# and PECP@Eqs. ~5!and~6!# are identical. The magnetic field applied on MSCPsimulated by electric field. The quality of interface in Mcomposite is one key factor for obtaining large ME outpThe calculations show that there is no electric outputPECP if PECP is not bonded with MSCP. Here, the perfbonding of MSCP and PECP was considered, then the etric voltage, stress, and displacement as well would besame at the interface between MSCP and PECP in the cputation. Because the magnetic domain orientation of MSand the applied magnetic field are along the longitudinalrection, the right surface of MSCP are grounded, i.e.,voltages are set zero. The ac electrical voltage load is appon the left surface of MSCP to simulate the applied ac mnetic field on MSCP. Since the poling of PECP is in ttransverse direction, the voltage degrees of freedom atbottom surface are grounded, and the voltage degrees ofdom at the top surface of PECP except its left surfacecoupled. In order to reduce the relative error of calculatithe division number of PECP along its longitude directishould be enough large.

The constitutive relations for both MSCP and PEChave the same form. Based on Eqs.~2!–~6!, one understandsthat the ME effect of the structure originates from the mchanical coupling: the magnetic field induces the stressdisplacement of MSCP@Eq. ~2!#, and the stress and displacment of PECP are transferred from MSCP through the boing interface, then the electric field is generated by the stand displacement in PECP@Eq. ~6!#.

The finite element algorithm is a powerful tool to predthe dynamic behavior of the ME structure under ac magnfield. The general FEM equations of piezoelectric materare given by

Md̈1Kld1Kff5F, ~7!

KfTd1K2f5Q, ~8!

whered andf are the node displacement and electric pottial; M, K1 , Kf , and K2 are the mass matrix, the elaststiffness matrix, the electric–elastic coupling matrix, andelectric field matrix, respectively;F andQ are the equivalennode force and electric displacement. The general Fequations for the magnetostrictive and piezoelectric matals should have the same form, as given by Eqs.~7! and~8!.

A full harmonic response analysis ofANSYS5.5/Multiphysics was used to determine the resonance frequeof the ME structure driven by an ac magnetic field for otaining the strong ME output. The main parameters forsystem properties are given in the Appendix. The procedof finite element analysis is presented in the following:

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~1! Element type: coupled-field solid element is chosencalculate the mechanical-electric coupling.

~2! Material properties: a complete description of constitive relation of PECP includes the anisotropic elastic mtrix, piezoelectric matrix, and dielectric matrix. The bhavior of MSCP is calculated in a similar mannebecause the constitutive equations for magnetostricmaterials and piezoelectric ones are similar, althoughformer cannot be simulated directly byANSYS5.5. Thecorresponding constitutive description of MSCP includthe anisotropic elastic matrix, magnetostrictive matrand permeability matrix. The two sets of constitutive prameters and density for MSCP and PECP given inAppendix are determined based on the value scopevided by manufacturer.

~3! Meshing: the dimensions of the two componentsgiven in the following sections. The bonding of MSCand PECP is performed by the glue operation inANSYS.The finer element is, the more time is cost althoughresults would be more accurate. Through the pilot callation, the divided numbers of MSCP are determined7(L)35(W)32(T), and those for PECP are 8 – 13(L)35(W)32(T).

~4! Boundary condition: three zero displacements inz~thick-ness! direction, two zero displacements inx~length! di-rection, and one zero displacement iny~width! directionare applied to restrict the rigid motion. The bottom suface of PECP and the right surface of MSCP agrounded, i.e., the voltages are set zero. The voltagegrees of freedom at the top surface of PECP exceptat its left surface are coupled. The ac electrical voltaload is applied on the left surface of MSCP to simulathe applied ac magnetic field on MSCP because MSCsimulated by PECP.

~5! A frontal solver was selected to solve the finite elemeequation given in Eqs.~6! and ~7!.

~6! Covered range of frequency: for single-phase materithe frequency ranges between 30 and 140 kHz; fortwo-phase case, it covers from 30 to 120 kHz.

~7! Effect of magnetic bias: the magnetic bias would induthe variation of magnetoelastic coupling coefficients athe stress in MSCP, then the response of the ME coposite to the ac magnetic field would be equivalent toprestressed material. The influence of the magnetic bon magnetoelastic coupling coefficients was considein this article, although the harmonic response analyof prestressed PZT material could not be performedANSYS5.5.

III. NUMERICAL RESULTS AND COMPARISON WITHEXPERIMENTS

From the experimental point of view, the optimizecomposite structure is one with identical resonancequency for both MSCP and PECP. The resonance frequeof MSCP corresponds to the largest relative permeabilityder an ac magnetic field, and at the resonance frequencPECP the current~or the impedance! under an ac electricfield load reaches the maximum~or the minimal!. First, wecalculate the resonance behavior for MSCP and PECP s

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rately, supposing that they are not bonded together. Incalculation, the amplitude of magnetic field and that of eltric field applied to MSCP and PECP are set as 1.8 Oe1.0 V, respectively. By setting the dimensions of MSCPL57.0,W56.6, andT51.0, referring to the real dimensionof MSCP in our experiment, the calculated induction eleccurrent~corresponding to relative permeability! as a functionof magnetic signal frequency is shown in Fig. 3~a!, predict-ing a resonance frequency of 106 kHz. The frequency sptrum and resonance behavior are quite similar to the expmental results, as shown in Fig. 3~b! where the resonancfrequency is 105.6 kHz, which demonstrates that the numcal procedure reproduces the experimental results withincalculation uncertainty.

For PECP, if the cross section (W3T) remains the sameas that of MSCP, the resonance frequency depends onlength ~L!. Through the pilot calculation, one obtains thresonance frequency of 106 kHz for a component of dimsions L513.3, W56.6 mm, andT51.0, as shown in Fig.4~a!. The above dimensions for PECP were determinedour experiment. The experimental data on the impedancefunction of frequency for PECP are plotted in Fig. 4~b!,where the resonance frequency is 104.2 kHz, very closthe calculated value. Subsequently, the composite strucfor our calculation consists of the two components optimizabove in terms of the identical resonance frequency.

When the two components are bonded together to cstitute a composite structure, the frequency spectra and rnance behaviors for both components may be different frthose presented above for two unbonded components.the composite structure activated by an applied magnfield, the calculated electric voltage output of PECP andresonance are given in Fig. 5~a!, from which several resonance points are identified, i.e.,21.51 V at 56 kHz, 4.4 V at

FIG. 3. Frequency spectrum of~a! electric current~corresponding to relativepermeability! and ~b! permeability for MSCP (7.0 mm36.6 mm31.0 mm).

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58 kHz, 10.5 V at 106 kHz, and26.4 V at 107 kHz. Thecalculated maximum voltage output is 10.5 V at 106 kHz.a driving magnetic field of 5.0 Oe, as employed in the eperiments, the predicted output is;28 V at 106 kHz. Experi-mentally, the output at resonance frequency was found to16.0 V at 55.7 kHz and 19.9 V at 109 kHz, as shown in F

FIG. 4. Frequency spectrum of~a! polarization electric current and~b! im-pedance for PECP (13.3 mm36.6 mm31.0 mm).

FIG. 5. Frequency spectrum of voltage output for the ME composite stture ~MSCP 7.0 mm36.6 mm31.0 mm, PECP 13.3 mm36.6 mm31.0 mm),~a! calculation, and~b! experiment.

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5~b!. A rough consistence of the calculated output with tmeasured value is shown, although the calculated onlarger. Because the thickness of PECP isT51.0, the calcu-lated maximum ME output is 5.83 V/~Oe mm! at 106 kHz,slightly larger than the measured maximum ME output3.98 V/~Oe mm! at 109 kHz. Though the quantitative diffeence in the ME output exists, the calculated resonancequency remains quite similar. Therefore, it is demonstrathat the present FEM numerical technique works wellpredicting the ME behaviors of ME-composite structure,addition to the components alone.

IV. MECHANICAL COUPLING AND OPTIMUM DESIGN

The two components MSCP and PECP interact bymechanical coupling on the bonded interface via Eq.~1!. Theoptimizing concept employed experimentally for the ME efect is to adjust the component dimensions so that both cponents have the same resonance frequencyf 0 at somemode. Since a reliable measurement of displacement athe bonded interface between MSCP or PECP is challengthe resonance is probed experimentally by impedancefor PECP and magnetic susceptibility scan for MSCP. At tsame resonance frequency for the two components theplacement quantities at the two sides of the bonded intermust be the same due to the interface coupling. Howevef 5 f 0 , both MSCP and PECP resonate but the activatedplacements may not be equivalent, depending on the dimsions of the two components, respectively. The mechancoupling may not be sufficient, so that the activated Moutput is not at the maximum mode. One needs to develooptimum procedure in order to calculate the possible mamum mechanical coupling.

Experimentally, the source load for the PECP is the eltric field, while in the ME composite structure the electrsignal is the output while the source load is the displacemor stress on the left surface. The number of vibration mofor the ME structure is unlimited, and different vibratiomodes can be activated by imposing different loads. Oargument is that the dimensions of PECP should be omized, on the basis of the displacement response ofMSCP to magnetic field and the voltage response ofPECP to the displacement load activated on its left surfaFor the ME structure shown in Fig. 1, the main effectidisplacement would be the displacement in thex ~length!direction.

First, let us see an example to show the differenGiven fixed dimensions of MSCP withL57.0, W56.6, andT51.0, we calculate the displacement amplitudeUx in xdirection as a function of frequencyf of the magnetic fieldfor MSCP component at the bonded interface, as illustrain Fig. 6~a!. The predicted two extreme points are21.4731027 m at 85 kHz, and 3.4431026 m at 106 kHz. SetUx

for PECP (L513.3,W56.6, andT51.0) at the bonded in-terface as 1.031026 m ~corresponding to a frequency of 6kHz!, the voltage output of PECP as a function of frequenis shown in Fig. 6~b!, where the maximum voltage output26136 V at 60 kHz. The voltage is too high to be reliab

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but it allows us to argue that the voltage output from PEcan be much higher than the experimentally measured vaWe see also that the resonance frequency for PECP is 60at which the displacement of MSCP is 1.031026 m.

A rough calculation shows us a resonance frequency85 kHz if L59.4 mm, and 106 kHz ifL57.5 mm. It isunderstandable that for the composite structure, the mainfective displacement isUx , whereas the displacements inyand z direction would have a certain degree of influencThus the lengthL for PECP exhibiting the maximum voltagoutput would not be exactly 7.5 or 9.4 mm, but some vaclose to them.

The pilot calculation tells us that the optimized value fL near 9.4 mm at which the voltage output reaches the mmal is 9.6 mm. The calculated frequency spectrum is shoin Fig. 7~a! whereL59.6 mm. The two extreme points ar2100.8 V at 64 kHz, and 2.13 V at 65 kHz. The maximuoutput decreases very fast ifL deviates from 9.6 mm. For afurther comparison, asL59.4 and 10.0, the calculated frequency spectra are shown in Figs. 7~b! and 7~c!, respectively.The maximum voltages are24.3 V at 64 kHz, and 3.9 V at65 kHz, asL59.4 mm. They are27.86 V at 63 kHz, and2.62 V at 64 kHz asL510.0 mm.

In the similar way, whenL takes a value close to 7.mm, the pilot calculation shows the maximum voltage ifL58.0 mm, as shown in Fig. 8, where the two extreme poiare273.6 V at 68 kHz, and 2.3 V at 69 kHz. On the othhand, given the dimensions of MSCP, one may argue thatvoltage output would be stronger if the length of PECPlonger. In order to clarify this point, the calculation has beperformed. AsL517.0 mm, the maximum output are21.37V at 50 kHz, 5.24 V at 51 kHz, 6.14 V at 92 kHz, and27.0V at 93 kHz. Obviously the output asL517.0 mm is much

FIG. 6. ~a! Calculated displacement in x direction as a function of frequenfor MSCP (7.0 mm36.6 mm31 mm) induced by a magnetic field in x direction; ~b! calculated voltage output from PECP (13.3 mm36.6 mm31.0 mm) activated by the displacement at the bonded interface.

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smaller than that asL59.6 and 8.0 mm, smaller than thexperimental result too.

As a summary, the calculated maximum voltage outand the lengthL of PECP for the composite structureshown in Fig. 9. It is clearly indicated that the optimizedimensions for the two components are 7.0 mm36.6 mm31.0 mm for MSCP, and 9.6 mm36.6 mm31.0 mm forPECP. The maximum ME output is 8.6 times the expe

FIG. 7. Calculated frequency spectra of the voltage output for the compstructure at different length of PECP component.~a! MSCP: 7.0 mm36.6 mm31.0 mm, PECP: 9.6 mm36.6 mm31.0 mm; ~b! MSCP:7.0 mm36.6 mm31.0 mm, PECP: 9.4 mm36.6 mm31.0 mm; ~c! MSCP:7.0 mm36.6 mm31.0 mm, PECP: 10.0 mm36.6 mm31.0 mm.

FIG. 8. Calculated frequency spectra of the voltage output for the compstructure~PECP: 8.0 mm36.6 mm31.0 mm).

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mentally measured output. Based on these numerical reswe could draw the conclusion that the ME composite strture should be optimized in terms of the mechanical couplmechanism for its surprising ME output. This numerical prcedure could be applied to other ME structures wheremechanical coupling mechanism plays a key role.

V. CONCLUSION

The numerical simulation has been put forward forME-composite structure developed experimentally earlFirst, the ME coupling mechanism and numerical simulatprocedure for this structure has been presented. The numcal simulation agrees well with the experimental resultshas been proposed that the ME output must be optimiaccording to the mechanical coupling mechanism by whthe magnetostrictive component and piezoelectric componinteracts with each other. This numerical procedure has bproved to be an essential counterpart to the experimeoptimization in order to achieve the maximum ME output

ACKNOWLEDGMENTS

The authors would like to acknowledge the financsupport from the National Key Project for Basic Researcof China ~2002CB613303!, the National Natural ScienceFoundation of China through the Innovative Group Projand Normal Project, and LSSMS of Nanjing Universitywell.

APPENDIX

A. Material properties of PECP

~1! Anisotropic elastic matrix

37.97 3.58 3.58 0 0 0

3.58 7.97 3.58 0 0 0

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0 0 0 0 0 1.44

4 31010 Pa

ite

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FIG. 9. Maximum voltage output of the ME composite structure as a fution of the lengthL of PECP~MSCP: 7.0 mm36.6 mm31.0 mm, PECP:L36.6 mm31.0 mm).

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~2! Piezoelectric matrix

30 0 25.9

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4 3N/~V m!

~3! Dielectric matrix

F 15.92 0 0

0 15.92 0

0 0 15.92G31029 A~s/V m!

~4! Density: 7700 kg/m3

B. Material properties of MSCP

~1! Anisotropic elastic matrix

33.11 1.52 1.52 0 0 0

1.52 3.56 1.52 0 0 0

1.52 1.52 3.56 0 0 0

0 0 0 1.36 0 0

0 0 0 0 1.36 0

0 0 0 0 0 1.57

4 31010 Pa

~2! Magnetostrictive matrix

3156.8 0 0

260.9 0 0

260.9 0 0

0 0 0

0 0 108.3

0 108.3 0

4 3N/~A m!

rticle is copyrighted as indicated in the article. Reuse of AIP content is sub

87.66.108.143 On: Tue,

~3! Permeability matrix

F 5.4 0 0

0 5.4 0

0 0 5.4G31026 V~s/A m!

~4! Density: 9200 kg/m3

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