ABSTRACT
The vibration theory is well developed for nonelectrical shells: different types of vibrations are distinguished, approximate theories are constructed for describing every type, and the errors are estimated. In this chapter, the author uses the asymptotic method for integrating the dynamic equations of the piezoceramic shells theory. She writes only the asymptotics of the stressed-strained state and the asymptotic estimates of the accuracy of the approximate theories for the remaining types of vibration. When integrating the auxiliary problem equations, the tangential boundary conditions should be met. In the approximate equations of the principal and auxiliary problems, the author neglects any function as compared to its derivative within quantities of order; and treats the quantities that describe the shell geometry as constants. The free vibrations of an arbitrary piezoceramic shell can be subdivided into quasitransverse, quasitangential, and low frequency Rayleigh-type vibrations.
