Full Text:   <3038>

CLC number: O326; O343.8; TU411.8

On-line Access: 

Received: 2005-03-01

Revision Accepted: 2005-04-20

Crosschecked: 0000-00-00

Cited: 0

Clicked: 5344

Citations:  Bibtex RefMan EndNote GB/T7714

-   Go to

Article info.
Open peer comments

Journal of Zhejiang University SCIENCE A 2005 Vol.6 No.9 P.938-944


Analytical modelling and free vibration analysis of piezoelectric bimorphs

Author(s):  ZHOU Yan-guo, CHEN Yun-min, DING Hao-jiang

Affiliation(s):  Department of Civil Engineering, Zhejiang University, Hangzhou 310027, China

Corresponding email(s):   qzking@zju.edu.cn, cym@civil.zju.edu.cn

Key Words:  Piezoelectric bimorph, Analytical model, Free vibration, Shear correction factor, First-order shear deformation theory

ZHOU Yan-guo, CHEN Yun-min, DING Hao-jiang. Analytical modelling and free vibration analysis of piezoelectric bimorphs[J]. Journal of Zhejiang University Science A, 2005, 6(9): 938-944.

@article{title="Analytical modelling and free vibration analysis of piezoelectric bimorphs",
author="ZHOU Yan-guo, CHEN Yun-min, DING Hao-jiang",
journal="Journal of Zhejiang University Science A",
publisher="Zhejiang University Press & Springer",

%0 Journal Article
%T Analytical modelling and free vibration analysis of piezoelectric bimorphs
%A ZHOU Yan-guo
%A CHEN Yun-min
%A DING Hao-jiang
%J Journal of Zhejiang University SCIENCE A
%V 6
%N 9
%P 938-944
%@ 1673-565X
%D 2005
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2005.A0938

T1 - Analytical modelling and free vibration analysis of piezoelectric bimorphs
A1 - ZHOU Yan-guo
A1 - CHEN Yun-min
A1 - DING Hao-jiang
J0 - Journal of Zhejiang University Science A
VL - 6
IS - 9
SP - 938
EP - 944
%@ 1673-565X
Y1 - 2005
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.2005.A0938

An efficient and accurate analytical model for piezoelectric bimorph based on the improved first-order shear deformation theory (FSDT) is developed in this work. The model combines the equivalent single-layer approach for mechanical displacements and a layerwise-type modelling of the electric potential. Particular attention is devoted to the boundary conditions on the outside faces and to the interface continuity conditions of the bimorphs for the electromechanical variables. shear correction factor (k) is introduced to modify both the shear stress and the electric displacement of each layer. And the detailed mathematical derivations are presented. free vibration problem of simply supported piezoelectric bimorphs with series or parallel arrangement is investigated for the closed circuit condition, and the results for different length-to-thickness ratios are compared with those obtained from the exact 2D solution. Excellent agreements between the present model prediction with k=8/9 and the exact solutions are observed for the resonant frequencies.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


[1] Chee, C.Y.K., Tong, L., Steven, G.P., 1998. A review on the modeling of piezoelectric sensors and actuators incorporated in intelligent structures. Journal of Intelligent Material Systems and Structures, 9:3-19.

[2] Cowper, G.R., 1966. The shear coefficient in Timoshenko’s beam theory. Journal of Applied Mechanics, 33:335-340.

[3] Ding, H.J., Wang, G.Q., Chen, W.Q., 1997. Green’s functions for a two-phase infinite piezoelectric plane. Proceedings of the Royal Society Series A, 453:2241-2257.

[4] Fernandes, A., Pouget, J., 2003. Analytical and numerical approaches to piezoelectric bimorph. International Journal of Solids and Structures, 40:4331-4352.

[5] Gopinathan, S.V., Varadan, V.V., Varadan, V.K., 2000. A review and critique of theories for piezoeletric laminates. Smart Materials and Structures, 9:24-48.

[6] Ha, S.K., Kim, Y.H., 2002. Analysis of a piezoelectric multi-morph in extensional and flexural motions. Journal of Sound and Vibration, 253(5):1001-1014.

[7] He, L.H., Lim, C.W., Soh, A.K., 2000. Three-dimensional analysis of an antiparallel piezoelectric bimorph. Acta Mechanica, 145:189-204.

[8] Lim, C.W., He, L.H., Soh, A.K., 2001. Three-dimensional electromechanical responses of a parallel piezoelectric bimorph. International Journal of Solids and Structures, 38:2833-2849.

[9] Rao, S.S., Sunar, M., 1994. Piezoelectricity and its use in disturbance sensing and control of flexible structures: a survey. Applied Mechanics Reviews, 47:113-123.

[10] Shirley, D.J., Hampton, L.D., 1978. Shear-wave measurements in laboratory sediments. Journal of the Acoustic Society of America, 63(2):607-613.

[11] Smits, J.G., Dalke, S.I., Cooney, T.K., 1991. The constituent equations of piezoelectric bimorphs. Sensors and Actuators A-Physics, 28:41-61.

[12] Sosa, H.A., Castro, M.A., 1993. Electroelastic analysis of piezoelectric laminated structures. Applied Mechanics Reviews, 46:21-28.

[13] Timoshenko, S.P., 1922. On the transverse vibrations of bars of uniform cross-section. Philosophical Magazine, 6(43):125-131.

[14] Timoshenko, S.P., Yong, D.H., Weaver, W., 1974. Vibration Problems in Engineering (4th Ed). Wiley, New York.

[15] Wang, Q., Quek, S.T., Sun, C.T., Liu, X., 2001. Analysis of piezoelectric coupled circular plate. Smart Materials and Structures, 10:229-239.

[16] Wang, S.Y., 2004. A finite element model for the static and dynamic analysis of a piezoelectric bimorph. International Journal of Solids and Structures, 41:4075-4096.

[17] Yang, J.S., 1999. Equation for thick elastic plates with partially electroded piezoelectric actuators and higher order electric fields. Smart Materials and Structures, 8:73-82.

[18] Zhou, Y.G., Chen, Y.M., Huang, B., 2005. Experimental study of seismic cyclic loading effects on small strain shear modulus of saturated sands. Journal of Zhejiang University SCIENCE, 6A(3):229-236.

Open peer comments: Debate/Discuss/Question/Opinion


Please provide your name, email address and a comment

Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - 2023 Journal of Zhejiang University-SCIENCE