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.

采用等效弹性法对矩形压电陶瓷堆的三维耦合振动进行分析，该方法是一种近似解析方法。当忽略剪应力和应变时，通过定义三个机械耦合系数，将矩形压电陶瓷叠层的复杂耦合振动简化为三个一维耦合振动。在分析的基础上建立了三维机电等效电路。推导出决定压电振子振动模式的共振频率方程，计算出不同模式的共振频率。根据耦合振动的共振频率方程，长、宽、分析矩形压电陶瓷叠层在谐振频率上的厚度和厚度。制作了三组不同尺寸的矩形压电陶瓷堆进行实验和数值模拟。结果表明，理论结果与实验分析和仿真结果吻合较好，为拓展矩形压电振子的应用提供了理论支持。