Nonlinear free vibration of piezoelectric semiconductor doubly-curved shells based on nonlinear drift-diffusion model

In this paper, the nonlinear free vibration behaviors of the piezoelectric semiconductor (PS) doubly-curved shell resting on the Pasternak foundation are studied within the framework of the nonlinear drift-diffusion (NLDD) model and the first-order shear deformation theory. The nonlinear constitutive relations are presented, and the strain energy, kinetic energy, and virtual work of the PS doubly-curved shell are derived. Based on Hamilton’s principle as well as the condition of charge continuity, the nonlinear governing equations are achieved, and then these equations are solved by means of an efficient iteration method. Several numerical examples are given to show the effect of the nonlinear drift current, elastic foundation parameters as well as geometric parameters on the nonlinear vibration frequency, and the damping characteristic of the PS doubly-curved shell. The main innovations of the manuscript are that the difference between the linearized drift-diffusion (LDD) model and the NLDD model is revealed, and an effective method is proposed to select a proper initial electron concentration for the LDD model.