Free vibration of a piezoelectric semiconductor plate

We analyze free vibration of a piezoelectric semiconductor (PSC) plate taking account of the coupling between deformation, polarization and carriers within the framework of the first-order shear deformation theory. The PSC plate is subjected to a biaxial force and an external electric voltage. The governing equations and corresponding boundary conditions are derived using Hamilton principle. An analytical solution for a simply supported PSC plate is obtained. A detailed parametric study is conducted to discuss the effects of steady-state carrier density, axial force, external electric voltage, length-to-thickness ratio and length-to-width ratio on the free vibration characteristics of the PSC plate. The numerical results show that the steady-state carrier density has a significantly influence on natural frequency of the PSC plate in a certain range. The vibration frequency decreases when the plate is subjected to the axial compression and the positive external voltage. The vibration frequency increases with the increase of length-width ratio of and also increases with the decrease of length-thickness ratio of the PSC plate. This work may be useful for the analysis and design of electron devices made from PSC materials.