Axisymmetric Vibration of Piezoelectric Semiconductor Disc Based on Double Legendre Polynomial Method

Piezoelectric semiconductors (PSCs) have attracted much attention in recent years for combining piezoelectric with semiconducting properties. As far as we know, there is very limited theoretical research on the vibration problem of three-dimensional PSC disc structure. In this paper, a double Legendre polynomial method was developed to analyze axisymmetric free vibration for axially polarized PSC disc. The present method directly incorporated the boundary conditions into the control equations of PSC. Simultaneously, the mechanical displacements, the electrical potential and the carrier density were defined as the form of double Legendre polynomials series. Then, the natural frequencies are obtained through solving eigenvalue. The numerical example shows that the steady-state carrier density has important influence on the natural frequency only in a certain range, and the effect on the higher modes is more obvious than the lower modes. Finally, the effects of radius-to-thickness ratio on the frequencies were also studied.