As a complex electromechanical coupling system, studying the impact of nonlinearity on the performance and stability of piezoelectric ultrasonic actuators is a highly significant topic. A novel kinetic model for the piezoelectric ultrasonic actuator is established, taking into account nonlinear factors such as surface roughness and elastic-plastic contact. Firstly, the multiple scales method is adopted to obtain the accurate approximate time-response and to elucidate the relationship between frequency and phase-amplitude. Based on this relationship, the steady-state response equation is presented, and the steady-state solution of the system and its stability are analyzed. The saddle-node bifurcation set of the system is solved by the stability discriminant condition. Critical bifurcation points are characterized in accordance with the frequency, damping coefficient and excitation amplitude. Secondly, the phase resonance condition of the piezoelectric ultrasonic actuator is investigated, and the frequency corresponding to the maximum response amplitude is obtained. Finally, experiments and simulations are conducted to verify the accuracy of the model. The results demonstrate that this model can provide guidance for the control and optimization of the piezoelectric ultrasonic actuator.
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