Asymptotic Solutions of Boundary Value Problems of Electroelasticity for Transversely Isotropic Toroidal Shells Made of Piezoceramic Materials

Abstract

By asymptotic integration of the equations and relations of a three-dimensional problem of electroelasticity theory for transversely isotropic ceramics, boundary-value problems for a thin toroidal shell are solved in the cases where the conditions of the first, second, or mixed dynamic boundary-value problems of elasticity theory are given on its surface. Recurrent formulas for calculating components of the displacement vector and stress tensor and the electric field potential in thickness-polarized ceramics are deduced. The resonance frequencies are also found.