Abstract
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 withk=8/9 and the exact solutions are observed for the resonant frequencies.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
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.
Cowper, G.R., 1966. The shear coefficient in Timoshenko’s beam theory.Journal of Applied Mechanics,33:335–340.
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.
Fernandes, A., Pouget, J., 2003. Analytical and numerical approaches to piezoelectric bimorph.International Journal of Solids and Structures,40:4331–4352.
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.
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.
He, L.H., Lim, C.W., Soh, A.K., 2000. Three-dimensional analysis of an antiparallel piezoelectric bimorph.Acta Mechanica,145:189–204.
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.
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.
Shirley, D.J., Hampton, L.D., 1978. Shear-wave measurements in laboratory sediments.Journal of the Acoustic Society of America,63(2):607–613.
Smits, J.G., Dalke, S.I., Cooney, T.K., 1991 The constituent equations of piezoelectric bimorphs.Sensors and Actuators A-Physics,28:41–61.
Sosa, H.A., Castro, M.A., 1993. Electroelastic analysis of piezoelectric laminated structures.Applied Mechanics Reviews,46:21–28.
Timoshenko, S.P., 1922. On the transverse vibrations of bars of uniform cross-section.Philosophical Magazine,6(43): 125–131.
Timoshenko, S.P., Yong, D.H., Weaver, W., 1974. Vibration Problems in Engineering (4th Ed). Wiley, New York.
Wang, Q., Quek, S.T., Sun, C.T., Liu, X., 2001. Analysis of piezoelectric coupled circular plate.Smart Materials and Structures,10:229–239.
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.
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.
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
Project (Nos. 10472102 and 10372089) supported by the National Natural Science Foundation of China
Rights and permissions
About this article
Cite this article
Yan-guo, Z., Yun-min, C. & Hao-jiang, D. Analytical modelling and free vibration analysis of piezoelectric bimorphs. J Zheijang Univ Sci A 6, 938–944 (2005). https://doi.org/10.1631/jzus.2005.A0938
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1631/jzus.2005.A0938
Key words
- Piezoelectric bimorph
- Analytical model
- Free vibration
- Shear correction factor
- First-order shear deformation theory