Geometrically nonlinear axisymmetric response of thin circular plate under piezoelectric actuation

The objective of this study is to present an approximate analytical one-term Galerkin solution for the problem of nonlinear deflection, thermal buckling and natural frequencies of a three-layer thin circular plate made of an isotropic elastic core with piezoelectric layers bonded to its faces. The analysis is restricted to axisymmetric moderately large deflection of the plate subjected to a thermal load, radial edge load or edge displacement and actuated by applying an electric potential across a piezoelectric layer. The accuracy of this solution is assessed by comparison with the numerical series solution using collocation. The direct piezoelectric effect is neglected in the governing equations. The piezoelectric layers are assumed to be very thin and having Young's modulus and density much smaller than those of the elastic core. Hence, their stiffness and inertia are neglected. The rotational and inplane inertia and the shear deformation are neglected in the Von Karman type classical thin plate theory used in the analysis. Comparison with the collocation solution establishes that the Galerkin solution yields quite accurate results for the problems considered.