Keywords: piezoelectric, composite, cylinder, three-dimensional, elasticity, sensor, actuator.

In recent years, smart structures with piezoelectric sensors and actuators have attracted serious attention for they can sense and alter the mechanical response during an in-service operation. On the other hand, light-weight shell and panel structures may be one of the most popularly used structures in space vehicles. For these reasons, shell-type smart structures have become the focus for many researchers.

Tzou and his co-workers published a series of papers on finite element and analytical analysis of piezoelectric shell-type continua [1,2]. In addition to the aforementioned approximate analysis, exact studies of piezoelectric circular cylindrical shells [3] and piezothermoelastic shells [4] were also performed. The theories of plates and shells coupled with piezoelectricity theory were applied to piezoelectric sensor and actuator design by Lee [5]. The piezoelastic solutions to long cylindrical panel and shell structures were also presented by Kapuria [6]. Analysis of thick laminated panel with piezoelectric actuators and sensors based on three-dimensional theory of elasticity were presented [7,8]. The response analysis of the infinite piezoelectric shell panel actuators based on the theory of elasticity was also performed [9].

The objective of the present study is to investigate the elastic solution of cross-ply laminated cylinder with a piezoelectric layer using the three-dimensional theory of elasticity for the first time. The top piezoelectric layer is used as an actuator or sensor in differant states.

The cylinder is simply supported in the axial direction. It is subjected to pressure and electric excitation and a three dimensional elasticity solution is used.

The highly coupled partial differential equations (PDE) are reduced to ordinary differential equations (ODE) with variable coefficients by means of trigonometric function expansion in circumferential direction. The resulting ordinary differential equations are solved by the Galerkin finite element method. Finally a three layered cylinder with piezoelectric layers under the action of a dynamic load are solved and the results are compared with the latest published results.

1

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

2

Tzou H.S. , Zhong J.P., "Linear theory of piezoelectric shell vibrations", J Sound Vib. 175(1), 77-88, 1994. doi:10.1006/jsvi.1994.1312

3

Chen C.Q., Shen Y.P., "Piezothermoelasticity analysis for a cylindrical shell under the state of axisymmetric deformation", Int. J. Engng Sci. 34, No 14, pp. 1585-1600, 1996. doi:10.1016/S0020-7225(96)00053-5

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

Lee P.C.Y., 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

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

Daneshmehr A., Shakeri M., "Analysis of thick laminated panel with piezoelectric sensors based on three-dimensional theory of elasticity", ICTAM04 Conf. (IUTAM), Warsaw, Poland, 2004.

8

M. Shakeri, A. Daneshmehr, "Three dimensional elasticity solution for finite thick laminated shell panel with piezoelectric layers", J. Of Mech. En., Iran, 2004.

9

Daneshmehr A., Shakeri M., "The response analysis of the piezoelectric shell panel actuators based on the theory of elasticity", ESDA04 Conf. (ASME), Manchester, United Kingdom, 2004. doi:10.1115/ESDA2004-58389

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