Traveling wave rotary ultrasonic motors (TRUMs) are widely used in various industrial processes due to their attractive features, such as compact structure, high accuracy, and fast response. However, the major limiting factors of the operational performance of TRUMs under high-voltage excitation are the nonlinear behavior caused by the nonlinearities of the piezoelectric materials and the friction between the stator and rotor of the motor. In this study, a nonlinear dynamics model and an identification method are presented to directly design the driver circuit for suppressing the nonlinear behavior under high voltage excitation. Firstly, by studying the time–frequency characteristics of the isolated electrode voltage, a single-sided Hertzian contact forced oscillator model of TRUMs is established, involving the nonlinearities of the piezoelectric material and friction. Secondly, a harmonic balance nonlinear identification is proposed in the time domain for TRUMs. The influence of the voltage and preload on the nonlinear phenomena is discussed. Lastly, a novel driver circuit is proposed to suppress the nonlinearities using feedback from the isolated electrode. Experiments showed that the total harmonic distortion decreased by 89.4% under 500 Vpp. The proposed drive circuit design method is used to find a high excitation voltage and preload to achieve greater motor output power.