A study on the elasticity solution of the functionally graded (FG) shell with two piezoelectric layers is presented. In this article, the structure is finitely long, simply supported, and FG with two piezoelectric layers under pressure and electrostatic excitation. The equations of equilibrium, which are coupled partial differential equations, are reduced to ordinary differential equations (o.d.e.) with variable coefficients by means of trigonometric function expansion in the longitudinal direction. The resulting o.d.e. are solved by the Galerkin finite-element method and the Newmark method. Numerical results are presented for a FG cylindrical shell with a piezoelectric layer as an actuator in the external surface and a piezoelectric layer as a sensor in the internal surface.
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