Лоза И.А. «Неосесимметричные колебания полого неоднородного шара с пьезокерамическими слоями» Доповiдi нацiональноi академii наук Украiни, № 11, с. 76-83 (2011)

The problem of nonaxisymmetric natural vibrations of a hollow multilayered sphere with piezoceramic layers polarized in the radial direction is considered. The numerical-analytical method is offered for solving this problem. The initial problem of electroelasticity theory with partial derivatives after expanding the components of the stress tensor, displacement vector, electric induction, and electrostatic potential in spherical functions is reduced to the boundary-value problem for the system of ordinary differential equations for the radial coordinate. The problem is solved by a stable numerical method of discrete orthogonalization coupled with the incremental search method. The numerical results are presented for natural frequencies of vibrations in a wide range of the geometric characteristics of multilayered spheres.