Nonlinear Resonance Analysis And Simulation Of Piezoelectric Thin Plates Under The Thermoelastic Coupling Effect

Piezoelectric materials play an unique role in aviation,aerospace,electronic equipment,biotechnology and many other areas,for the unique attribute of dielectric effect and an inherent coupling effect between electrical and mechanical domains.Intelligent structures made of piezoelectric materials are widely used in these fields.Piezoelectric materials often experience large deformation and vibration under the multiple physical fields such as external excitation loads and temperature field work together.In order to ensure the safety and the stability of the structures,it is important to study its non-linear vibration characteristics.In this paper,the nonlinear resonance responses of piezoelectric elliptic and circular thin plates under thermoelastic coupling are studied.Firstly,taking the piezoelectric elliptic thin plate as an example,based on the Von-Karman plate theory of large deflection,the nonlinear governing equation of the piezoelectric elliptic thin plate under the combined action of external harmonic excitation and temperature field is derived by using the Bubnov-Galerkin method.Then,the amplitude-frequency response equations and the first order approximate solutions of the piezoelectric elliptic thin plate under superharmonic and subharmonic resonances are further obtained by means of the multi-scale method.The stability conditions of the steady solution are determined according Routh-Hurwitz criterion.The effects of the temperature difference at the plate center,the effective damping coefficient,the external excitation amplitude,the plate thickness and the ratio of semi-major axis to semi-minor axis on superharmonic and subharmonic resonances behaviours of piezoelectric elliptic thin plate are analysed by MATLAB.It is found that the resonant amplitude and the coexistence region of multiple solutions decrease for the superharmonic resonance,the resonant amplitude increases,while the distance between the two branches of the amplitude-frequency response curve do not change significantly for the subharmonic resonance,as the temperature difference at the plate center increases.The softening/hardening nonlinearity characteristics of the system are determined by the ratio of semi-major axis to semi-minor axis of piezoelectric elliptic thin plate.Secondly,similarly,the nonlinear dynamic equation of piezoelectric circular thin plate under temperature field and external excitation is established in polar coordinates.The amplitude-frequency response equation and phase-frequency response equation are obtained by multi-scale method when the primary resonance occurred.The influence of the temperature difference at the plate center,the effective damping coefficient,the external excitation amplitude,the plate thickness on the primary resonance behavior is analyzed by MATLAB.Moreover,the thermal stress,modal,harmonic response and transient dynamics analysis are performed by ANSYS software,which further verified the correctness of the theoretical derivation.The effects of the temperature difference at the plate center,external excitation frequency and damping on the transverse displacement and velocity of piezoelectric circular plate are discussed in detail.The research shows that the natural frequency of the system increases with the increase of the thickness and the temperature difference at the plate center.The transverse displacement and transverse velocity of the plate center increase with the increase of the temperature difference at the plate center.