Asymptotic solution of the electroelasticity problem for thickness-polarized piezoceramic shells

Recurrence formulae for determining the components of the stress tensor, the displacement tensor and the electric potential of a piezoceramic shell are derived by asymptotic integration of the equations of the three-dimensional problem of the theory of electroelasticity in curvilinear coordinates. The shell is assumed in plan to be inhomogeneous (the physical-mechanical coefficients may depend on the tangential coordinates, but are constant across the thickness) and is thickness-polarized. The cases when conditions of the first, second or mixed boundary conditions of the theory of elasticity are specified on the outer and inner surfaces are considered. Dispersion equations of the vibration frequencies are derived for a comparatively general version, the values of the resonance frequencies are calculated, and their dependence on the thickness and the physical-mechanical parameters of the shell is established.