Dynamic axisymmetric problem of the direct piezoeffect for a radially polarized anisotropic piezoceramic cylinder

An unsteady problem of electroelasticity for a long radially polarized anisotropic piezoceramic cylinder with normal stresses that are arbitrary functions of time applied to the radial surfaces is considered. A closed solution is constructed by the method of expansion with respect to eigen vector-functions. This solution allows determining the frequencies of natural oscillations, the stress-strain state of the element, and the potential and intensity of the induced electric field.