计及压电效应时矩形振子的三维振动研究

在计及压电效应的情况下，本文利用解析方法对有限尺寸压电陶瓷矩形振子的三维振动进行了研究，推出了振子耦合振动的频率方程，并对振子的振动模式进行了分析。理论研究表明，利用本文中的解析法研究振子的耦合振动，计算简单、物理意义明显。与传统的一维理论分析方法及数值方法相比，由于本研究考虑了振子的压电效应以及不同振动模式不同的相互耦合，因此，振子的理论计算频率与测量值更加符合。

Study on three dimensional vibration of piezoelectric ceramic rectangular resonators

An analytical method was presented to study the three dimensional vibration of piezoelectric ceramic rectangular resonators when piezoelectric effect was taken into account. The frequency equation was derived and the vibrational modes of the resonator were analyzed. It is shown that the method is simple and time-saving in the calculation and analysis of the coupled vibration of the resonators. Compared with traditional one dimensional theory and numerical methods, since the piezoelectric effect and the coupling among the longitudinal and transverse vibrations are taken into account in the analysis, the computed resonant frequencies are in good agreement with the measured results. Ir can be seen that the method and the conclusion will be useful in the design of resonators with large dimension, the measurement of material parameters and the analysis of vibrational mode of complex resonators.