Analysis on coupled vibration of piezoelectric ceramic stack with two piezoelectric ceramic elements

A longitudinally polarized piezoelectric ceramic stack with two piezoelectric ceramic elements is an important part of sandwich piezoelectric transducers. The three-dimensional coupled vibration of piezoelectric ceramic stack is analyzed. Since the longitudinal and radial dimensions of particular piezoelectric ceramic stacks are approximately equal, one-dimensional theory cannot be used for analysis. The piezoelectric ceramic stack is analyzed by the equivalent elastic method, which is an approximate analytical method, and it is considered that the coupled vibration of a piezoelectric ceramic stack is composed of equivalent radial and longitudinal vibrations. These two equivalent vibrations are connected by a mechanical coupling coefficient. The radial and longitudinal electromechanical equivalent circuits are obtained, and the resonance frequency equations are derived. The dependency of the radial and longitudinal resonance frequencies on the geometrical dimensions for piezoelectric ceramic stack is analyzed. The height or radius has a large influence on the longitudinal resonance frequency or the radial resonance frequency. Two sets of piezoelectric ceramic stacks are fabricated. The experimental results, COMSOL simulated results, and theoretical results are in good agreement.