Semi-analytical modeling and optimization of a traveling wave sandwich piezoelectric transducer with a beam-ring combined structure

Boasting the advantages of low maximum ground pressure and low locomotion resistance of tracked mechanisms, a traveling wave sandwich piezoelectric transducer with a beam-ring combined structure was proposed and developed to directly drive a metal track, and preliminary experimental investigations have confirmed the feasibility of the transducer design and its operating principle. However, the dynamic behavior of the sandwich piezoelectric transducer has not yet been studied theoretically. To enable practical applications, the sandwich piezoelectric transducer needs to be optimized for better output performances. Therefore, a semi-analytical model is of significance to describe the dynamic behavior of the sandwich piezoelectric transducer, to predict its driving effect, and to improve its output performance. In this study, an electromechanical coupling model is developed for the sandwich piezoelectric transducer by employing the transfer matrix method, in which a novel longitudinal-bending coupling vibration transfer matrix is created for the combined PZT elements and an in-plane bending vibration transfer matrix is developed for the closed curved beam element. To validate the proposed model, experimental investigations are carried out to measure the dynamic behavior of the transducer prototype and compare to calculation results. The differences between the measured and calculated resonant frequencies for two operating vibration modes are, respectively, 74 Hz and 63 Hz. Also the vibration shapes at the respective resonant frequencies match well. Comparisons demonstrate the feasibility of the developed transfer matrix model. To improve the output performance of the transducer, model-based optimization is conducted. The optimized geometrical sizes are obtained to meet optimization goals of the transducer.