Nonlinear superharmonic and subharmonic resonances of piezoelectric elliptic thin plates under thermoelastic coupling effect

Abstract

This paper aims at investigating the nonlinear vibration characteristics of the piezoelectric elliptic thin plate under the combined action of external harmonic excitation and temperature field. Based on the Von-Karman plate theory of large deflection, the nonlinear governing equation is derived by using the Bubnov-Galerkin method. Then, the amplitude-frequency response equations are further obtained using the multi-scale method, and the stability conditions of the steady solution are determined according to the Routh-Hurwitz criterion. The effects of the temperature difference at the plate center, the effective damping coefficient, the external excitation amplitude, and the ratio of the semi-major axis to the semi-minor axis on superharmonic and subharmonic resonances behaviors of the piezoelectric elliptic thin plate are analyzed. It is found that the coexistence region of multiple solutions and the resonant amplitude decrease for superharmonic resonance, as the temperature difference at the plate center increases. For subharmonic resonance, with the increase in the temperature difference at the plate center, the response amplitude increases, while the distance between two branches of the amplitude-frequency response curve has no obvious change. The softened/hardened nonlinear characteristics of the system are determined by the ratio of the semi-major axis to the semi-minor axis of the piezoelectric elliptic thin plate.