Primary resonance analysis of axially moving piezoelectric semiconductor thin plate in multi-physical fields

In this paper, the primary resonance problem of axially moving piezoelectric semiconductor thin plate is studied. As a new material, piezoelectric semiconductors are used in aerospace, signal transmission, new energy and other related engineering fields. At present, piezoelectric semiconductors have been developed to the third generation, and the main materials are zinc oxide (ZnO) and gallium nitride (GaN), which have the advantages of high thermal conductivity and high breakdown voltage. The equation of vibration for the thin plate is derived using Hamilton’s variational principle, based on geometric nonlinear hypothesis and the constitutive equation of piezoelectric semiconductor, and discretized via the Galerkin method. The amplitude–frequency response of the system is obtained by solving the governing equation based on multi-scale method, and the stability analysis of the system is given. The effects of different physical parameters on the primary resonance of the system and the dynamic characteristics of the multistable attractor are given by numerical analysis. The bifurcation theory and chaos phenomenon of axially moving piezoelectric semiconductor plate under multiple physical fields are studied. The global bifurcation diagrams of the system with excitation amplitude, axial velocity and other physical quantities are presented by numerical calculation, and verified by the maximum Lyapunov exponent diagram and Poincaré map. The influences of each bifurcation parameter on the bifurcation response and chaos motion of the system are obtained.