In this paper, the dynamic instability of a simple supported, fimite-length, laminated circular cylindrical shells subjected to parametric excitation by axial loading and covered by piezoelectric materials presented analytically. The shell is taken to be orthotropic and could be oriented at angles of 0˚ and 9˚ (cross-ply) or at +θ and -θ (angle-ply) with respect to the shell axis. The effect of transverse shear deformation shell theory. Unimodal approximation of so-lution is adopted, and several mode shapes are seleted to explain the effects of the piezoelectricity of materials, as well as the effects of the geomtric parameters on instability regions.

An analytical study for the piezothermoelastic behavior of a circular cylindrical shell laminated with a piezoelectric layer is presented. The solution is obtained through the Power Series Expansion method in conjunction with axisymmetric thermal and mechanical loadings expanded as Fourier series. Both the direct and the inverse piezoelectric effects are studied in detail. Results presented are valuable for both assessing numerical results (e.g. the finite element method) obtained fromapproximate methods and understanding the piezothermoleastic response of piezoelectric smart shells. It is develop analytical models for piezoelectric structures to pizothermoelectric shell structures must be careful.