Nonlinear analysis on electro-elastic coupling properties in bended piezoelectric semiconductor beams with variable cross section

Abstract

In this paper, the effects of nonlinear constitutive relation on the electro-elastic coupling behaviors in non-uniform piezoelectric semiconductor beams are investigated. On the basis of three-dimensional theory for piezoelectric semiconductor and double power series, one-dimensional bending model is developed. In order to deal with the nonlinear problem, a differential quadrature method based iteration procedure is proposed. Comparing with the results from finite element method, the proposed method has good convergence and high accuracy. In numerical analysis, the effects of nonlinearity and non-uniformity in piezoelectric semiconductor are discussed thoroughly. It is found the introduction of nonlinearity induces the loss of symmetric for all electrical field quantities but little changes the mechanical quantities. While the reduction of width along the length direction produces larger mechanical and electrical responses. Importantly, the effects of nonlinearity on the electrical field quantities are more evident in a piezoelectric semiconductor beam with rapidly varied cross section. Besides, we designed the piezoelectric semiconductor beams subject to double shear forces and a beam with locally varied cross section. In the designed structures, the potential barriers and wells are realized, which provide new approaches adjusting the electro-elastic behaviors in piezoelectric semiconductors. The study in this paper could be the guidance designing high performance electronic devices.