Keywords: piezoelectric, composite shell, orthotropic, elasticity solution, actuator, sensor.

With the development of smart composite material applications and adaptive structures with sensor-active capabilities, the performance and reliability of aeronautical and space structural systems can be further improved. Smart structures combine the superior mechanical properties of composite materials, as well as incorporating the inherent capability to sense and adapt their static and dynamic response, or continuously monitor the location and extent of damage (health monitoring). 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 [1].

Using Hamilton's principle and linear piezoelectricity, Tzou [2] derived the system equations for piezoelectric shell vibrations. There are many works in which the circular cylindrical piezoelectric shell under static axisymmetric load has been approximately solved [3,4]. In addition to approximate analysis, exact studies of piezoelectric circular cylindrical shell subjected to axisymmetric loading and simply supported boundary conditions has been presented [5]. The exact solution for finite simply supported transversely isotropic cylindrical shells subjected to thermo-electro-mechanical loading was presented [6]. Kapuria and his co-workers presented a three-dimensional static solution for simply-supported piezoelectric cylindrical shells subject to axisymmetric loading [7]. A three dimensional elasticity solution of orthotropic thick laminated cylindrical shells and panels subjected to dynamic loading has been presented [8]. In the same manner the static and dynamic solution for finite thick and thin laminated cylindrical shell with one piezoelectric layer as actuator or sensor and two orthotropic layers were obtained by authors the [9,10].

In the present work, the elastic solution of an axisymmetric cross-ply laminated cylindrical shell with two piezoelectric layers is presented. The shell is subjected to internal pressure loading and uniform electric excitation at the outer surface. The cylindrical shell with finite lenght is simply supported at both ends and three dimensional elasticity approach is used.

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 axial direction. The resulting ordinary differential equations are solved by the Galerkin finite element method with a linear shape function in thickness. The results for a four-layered cylindrical shell with two piezoelectric layers and two orthotropic layers under electro-mechanical load are presented. First, the results for one layered piezoelectric cylindrical shell are compared with the exact results of [6]. It is seen that a good agreement stands between the results and the differences are negligible. Then the results for a simply supported cylindrical shell with two orthotropic and two piezoelectric layers as sensor and actuator subjected to inner pressure and outer electrical loading are discussed and compared with similar ones in the literatures and F.E.M software results. From the above studies, it is observed that the multilayered shell with a sensor and an actuator layer can be used for micro /nano shape control purposes, influencing the deflection of structure and three-dimensional analysis of piezo-elastic behavior of structures is recommended even for thin laminated structures.

1

Shakeri C., Noori M.N. and Hou Z., "Smart Materials and Structures: A review", Mat for the New Millennum, Proc Mat. Eng. Conf., ASCE, 1996, PP.863-876.

2

Tzou H.S. and Zhong J.P., "Electromechanics and Vibrations of Piezoelectric Shell Distributed Systems", J. Dyn. syst. Meas. Control, Vol.115, No.3, 1993, PP. 506-517. doi:10.1115/1.2899129

3

Pinto Carreia I.F., Mota Soares C.M. and Mota Soares C.A., "Analysis of Piezolaminated Axisymmetric Shell: A Semianalytical Higher Order Model", Computational Methods for Shell and Spatial Structures, IASS-IACM2000, PP.1-19.

4

Brooks S. and Heyliger P., "Static Behavior of Piezoelectric Laminates with Distributed and Patched Actuators", J. Intelligent Mat. Systems Struct, Vol.5, 1994, PP.635-650. doi:10.1177/1045389X9400500507

5

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 Stuctures, Vol.33, No.30, 1996, PP. 4481-4494. doi:10.1016/0020-7683(95)00278-2

6

Kapuria S., Dumir P.C. and Sengupta S., "Exact piezothermoelastic axisymmetric solution of a finite transversely isotropic cylindrical shell", J. Computers & Struct., Vol. 61, No.6, 1996, pp. 1085-1099. doi:10.1016/0045-7949(96)00182-4

7

Kapuria S., Sengupta S. and Dumir P.C., "Three-dimensional Solution for Simply-supported Piezoelectric Cylindrical Shell for Axisymmetric Load", Comput. Methods in Appl. Mech. Engrg., Vol.140(1-2), 1997, PP.139-155. doi:10.1016/S0045-7825(96)01075-4

8

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

9

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

10

Shakeri M., Yas M.H. and Saviz M.R., "Elasticity solution for laminated cylindrical shell with piezoelectric layer", RACM-9 Conf., Varanasi, India, 2004.

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