Keywords: piezoelectric, panel, composite, orthotropic, shell, three-dimensional, sensor.

As a result of two characteristics, i.e. the direct piezoelectric effect and the inverse piezoelectric effect, piezoelectric materials are widely used in hydro- and electro-acoustics, communications and measurement technology. In recent years the novel usages of them as distributed sensors and actuators in active structure control as noise attenuation, shape control and vibration suppression have attracted serious attention. On the other hand, composite laminates are well known for their high stiffness and strength. Therefore, the integration of piezoelectric materials and structural composites has become the subject of focus in the area of smart materials and structures and numerous papers on this subject have been published.

The theories of plates and shells coupled with piezoelectricity theory were applied to piezoelectric sensor and actuator design [1]. System equations for piezoelectric shell vibrations were derived, using Hamilton's principle and linear piezoelectricity [2,3]. The piezoelastic solutions to long cylindrical panel and shell structures were also presented [4,5,6]. Elastic solution of orthotropic thick laminated cylindrical panels subjected to dynamic loading was obtained by authors [7]. Finally, elasticity solution for infinite thick laminated shell panel with piezoelectric actuator layer was presented by authors [8].

In this paper, the elastic solution of cross-ply laminated panel with piezoelectric layer is presented. The panel is subjected to dynamic pressure excitation and three dimensional elasticity solution is used.

The shell panel is simply supported at circumference edges and infinitely at axial direction. The highly coupled partial differential equations (p.d.e.) are reduced to ordinary differential equations (o.d.e.) with variable coefficients by means of trigonometric function expansion in circumferential directions. The resulting ordinary differential equations are solved by Galerkin finite element method. Finally three layered panels with piezoelectric sensor are solved and the results are compared with latest published results.

1

Lee P.C.Y. and Yu J.D., "Governing equations of piezoelectric plates with graded properties across the thickness", Proc. Annual IEEE Int. freq. control symp. , 623-631, 1996. doi:10.1109/FREQ.1996.559939

2

Tzou H.S. and Zhong J.P., "Electromechanics and vibrations of piezoelectric shell distributed systems", J Dyn syst. Meas control 115(3), 506-517, 1993. doi:10.1115/1.2899129

3

Tzou HS and Zhong JP., "Linear theory of piezoelectric shell vibrations", J. und Vib. 175(1), 77-88, 1994. doi:10.1006/jsvi.1994.1312

4

Chen C-Q, Shen Y-P, and Wang X-M, "Exact solution for orthotropic cylindrical shell with piezoelectric layers under cylindrical bending", Int. J. Solids struct. 33(30), 4481-4494, 1996. doi:10.1016/0020-7683(95)00278-2

5

Dumir P.C., Dube G.P., and Kapuria S., "Exact piezoelastic solution of simply-supported orthotropic circular cylindrical panel in cylindrical bending", Int. J. solids struct. 34(6), 685-702, 1997. doi:10.1016/S0020-7683(96)00047-9

6

Kapuria S., Sengupta S., and Dumir P.C., "Three-dimensional solution for simply-supported piezoelectric cylindrical shell for axisymmetric load", Compu. Methods in Appl. Mech. Eng. 140(1-2), 139-155, 1997. doi:10.1016/S0045-7825(96)01075-4

7

M. Shakeri, A. Alibiglu, and M.R. Eslami, "Elastisity solution for thick laminated anisotropic cylindrical panels under dynamic load", J. Mech. Eng. Sci. Vol. 216 Part C, I Mech E, 2002.

8

Shakeri M., Daneshmehr A. and Alibiglu A., "Elasticity solution for thick laminated shell panel with piezoelectric layer", EASEC-9 Conf., Bali, Indonesia, 2003.

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