Exact static analysis of a rotating piezoelectric spherical shell

This paper gives an exact analysis of a rotating piezoelectric spherical shell with arbitrary thickness. At first, three displacement functions are introduced to simplify the basic equations of a spherically isotropic, piezoelectric medium. By expanding the displacement functions as well as the electric potential in terms of spherical harmonics, the basic equations of equilibrium are converted to an uncoupled Euler type, second order ordinary differential equation and a coupled system of three second order ordinary differential equations. A general solution to the homogeneous equations of equilibrium is then derived. The static analysis of a rotating spherical shell is then performed and numerical example is presented. The project supported by the National Natural Science Foundation of China, the Zhejiang Provincial Natural Science Foundation, and the Japanese Committee of Culture, Education and Science.