Nonlinear Vibration Analysis For Coupled Thermo-piezoelectric-mechanical Of Piezoelectric Rectangular Thin Plates

As common components in engineering,piezoelectric laminates are widely used in aerospace,intelligent manufacturing and other fields.Meanwhile,the operation and control of precision instruments are influenced greatly by the changes of temperature in actual environment.Thus the thermo-electric-mechanical coupling should be considered in the modeling process of piezoelectric laminates.The vibration of piezoelectric laminates caused by the coupling of multiple physical fields in the environment is related to the service life of structure.Therefore,the nonlinear vibration analysis of piezoelectric laminates is important for engineering applications.A model of piezoelectric rectangular thin plates with the consideration of the coupled thermo-piezoelectric-mechanical effect is established.Based on the von Karman large deflection theory,the nonlinear vibration governing equation is obtained by using Hamilton's principle and the Rayleigh-Ritz method.The harmonic balance method(HBM)is used to analyze the first-order approximate response and obtain the frequency response function.The system shows the non-linear phenomena such as hardening nonlinearity,multiple coexistence solutions,and jumps.The effects of the temperature difference,the damping coefficient,the plate thickness,the excited charge,and the mode on the primary resonance response are theoretically analyzed.With the increase in the temperature difference,the corresponding frequency jumping increases,while the resonant amplitude decreases gradually.Finally,numerical verifications are carried out by the Runge-Kutta method.When the effects of damping and electrical external excitation are not taken into account,the static bifurcation diagram and the influence curve of temperature change on natural frequency are obtained.The natural frequency attains its minimum when the temperature difference is 6 ?,which corresponds to the critical temperature of the buckling configuration.Finally,the parametric equation of the homoclinic orbit of the system is obtained by using its non-linear vibration equation.The threshold of homoclinic bifurcation is obtained by Melnikov method and verified by numerical method.The results show that with the increase of temperature difference,the distance between the two potential wells increases,and the depth of the potential well and the height of the barrier also increase.When the excitation intensity is lower than the critical threshold predicted by Melnikov theory,the response is limited to a single asymmetric potential well.When the excitation intensity is greater than the critical threshold predicted by Melnikov theory,the homoclinic bifurcation will cause the double-well motion.The threshold curve of homoclinic bifurcation is significantly affected by the changes of temperature difference.When temperature increases,the threshold of interwell jump increases as well,and the parameter range of chaotic window becomes narrower.Increasing temperature that changes the system gradually from the coexistence of chaos and periodic response to the coexistence of periodic response will inhibit the generation of chaotic response.The results will expand the research scope of nonlinear vibration and provide a strategy controlling the motion state of structures.