Torsional Vibration Analysis of a Core-Shell Piezoelectric Semiconductor Rod

We study the torsional vibration of a core-shell-like rod consisting of an inner n-type semiconductor core without piezoelectricity and an outer piezoelectric dielectric layer. Based on the linearized three-dimensional equations of piezoelectric semiconductors (PSs), the one-dimensional torsional vibration equations of the core-shell-like PS rod are established. An analytical solution for the PS composite rod with isolated and open-circuit conditions at the two ends is presented. Numerical results show that the initial concentration of electrons, applied moments, geometrical parameter, and exciting frequency have an influence on the multi-field coupling responses, and there is an optimal ratio of the inner semiconductor’s radius to the rod’s one for the charge-torque coefficient.