Analysis of longitudinal and torsional resonance vibrations of a piezoelectrically excited bar by introducing piezoelectric loss coefficients

In this study, a method to develop a resonance vibration model of a piezo-bar with slanted ceramics is presented by considering piezoelectric loss coefficients. The vibration model reported here predicts natural frequencies and mode shapes for longitudinal and torsional modes. Analytical results for the longitudinal and torsional vibration displacements were formulated as a function of material and geometric properties. Parametrical analysis of the resonance vibration modes and the explicit solution of the vibration displacement provide a tool for improving the design and developing control schemes for devices such as ultrasonic motors that utilize this structure. Model calculations were compared with ATILA™ finite element analysis simulations and good agreements were found. The model and the formulas to find the resonance frequencies and to calculate the vibration displacement were verified for different design parameters. Although the model was developed for a slanted ceramic stator of a multimode ultrasonic motor, the method to develop the model can be utilized for other single-degree-of-freedom piezoelectric ceramic applications.