Size-dependent free vibration of piezoelectric semiconductor plate

In this paper, the size-dependent free vibration of a piezoelectric semiconductor plate is investigated within the framework of the nonlocal theory and piezoelectric semiconductor theory. The displacement, electric potential and perturbation of electron concentration are provided based on the first-order shear deformation theory. The two-dimensional governing equations including the equations of motion, Gauss's law and current continuity condition are obtained by introducing the plane stress assumption and integrating the three-dimensional governing equations along the thickness direction. The vibration of a simply supported piezoelectric semiconductor plate is achieved by solving the governing equations. Some numerical examples are presented to show the effect of the initial electron concentration, nonlocal parameter, plate thickness, length to thickness ratio and length to width ratio on the vibration of the piezoelectric semiconductor plate. The results indicate that the damping characteristic of the piezoelectric semiconductor plate can be effectively designed by adding the appropriate initial electron concentration. Also, both the nonlocal parameter and the geometric property have an important effect on the natural frequency and damping characteristic of the system.