Three-dimensional coupled vibration of the rectangular piezoelectric ceramic stack.

The three-dimensional coupled vibration of the rectangular piezoelectric ceramic stack is analyzed by adopting the equivalent elastic method, which is an approximate analytical method. When the shear stress and strain are ignored, the complex coupled vibration of the rectangular piezoelectric ceramic stack is simplified to three one-dimensional coupled vibrations by defining three mechanical coupled coefficients. The three-dimensional electromechanical equivalent circuit is established on the basis of the analysis. The resonance frequency equation which determines the vibration mode of the piezoelectric vibrator is derived and the resonance frequencies of different modes can be calculated. According to the resonance frequency equation of coupled vibration, the effects of the length, width, and thickness of the rectangular piezoelectric ceramic stack on the resonance frequency are analyzed. Three groups of the rectangular piezoelectric ceramic stack of different dimensions are made for experiments and numerical simulations. The results show that the theoretical results are in good agreement with the experimental analysis and simulation results, which provide theoretical support for expanding the application of rectangular piezoelectric vibrators.