Two-dimensional theory of piezoelectric shells considering surface effect

Two-dimensional (2D) general equations of piezoelectric shells with nano-thickness are presented in an orthogonal curvilinear coordinate system, in which the surface effect is considered by treat the shell as a bulk core plus two surface layers. The general 2D equations can be directly degenerated into those of particular shells such as flat plates, cylindrical shells and so on by setting the Lamé coefficients and the principal radii of curvature to certain values. Using the derived 2D equations of cylindrical shells, the free vibration of a radially polarized piezoelectric cylindrical shell of finite length is analyzed. Numerical results show that the surface effect has a remarkable influence on the natural frequency of the shell at the nano-scale.