Parametric Vibration Analysis Of Axially Moving Piezoelectric Rectangular Thin Plate Under Thermoelectric Force Field

Piezoelectric materials are widely used in vibration field due to their unique piezoelectric effect.The nonlinear vibration problems of piezoelectric structure appeared with the change of complex working environment,such as temperature field,electric field and force field.When the system is excited by external parameters,the internal parameters of the system will change periodically and cause parameter vibration.A strong vibration response will occurs when the excitation frequency is close to twice the natural frequency of the system.Due to the sensitivity of piezoelectric materials to the changes of environmental parameters,the parametric vibration problem of the system may be more complex.In this paper,the parametric vibration of an axially moving piezoelectric rectangular plate under multiple physical fields and the related unsteady dynamic problems are investigated.The mechanical model of an axially moving piezoelectric rectangular thin plate under multiple physical fields are established Based on Kirchhoff-Love thin plate theory and Von Karman theory,the expressions of strain energy,kinetic energy and external force work of the system are derived through the piezoelectric equation.The nonlinear vibration equation and electric potential compatibility equation of axially moving piezoelectric rectangular thin plate under multiple physical fields are derived according to Hamilton principle.The corresponding boundary conditions are selected and the parametric vibration equation of the system is obtained by the Galerkin integral method.The principal parametric resonance of an axially moving piezoelectric rectangular thin plate under the temperature and electric fields is studied.The multi-scale method is applied to solve the principal parametric resonance equation of the system,and the amplitude-frequency response equation under the principal parametric resonance state is obtained.The system stability conditions of the steady-state solution are derived by the Lyapunov stability theory.Based on the numerical analysis,the system amplitudefrequency characteristic curve and the characteristic curve of the amplitude changing with each parameter are obtained,and the influence of the parameter change on the system principal parametric resonance characteristics are investigated.The principal parameter-principal combination resonance of an axially moving piezoelectric rectangular thin plate under the temperature,electric and mechanical fields are studied.The multi-scale method is applied to solve the system combination resonance equation.Two different resonance states and corresponding amplitudefrequency response equations are obtained by analyzing the secular term respectively.The amplitude-frequency characteristic curve and the regular curve of amplitude changing with voltage,center temperature difference,damping and other parameters are obtained by numerical calculation.The influence of parameters variation on the system combination resonance characteristics are analyzed.The bifurcation and chaos problem under the principal parametric resonance state and principal parameter-principal combination resonance state are studied.The bifurcation law and the system dynamic response under different bifurcation control parameters such as Poincare cross section,phase trajectory,and time history response under different bifurcation control parameters are analyzed by numerical calculation.The influence of system parameters on chaos threshold and bifurcation characteristics are studied.