压电梁弯曲振动方程及等效体力的计算

Flexure Vibration Equation of Piezoelectric Beam and Calculation of Equivalent Volume Force

目的 为研究石英音叉型角速率传感器提供设计参数方法 根据压电理论和弹性力学理论,讨论石英晶体振梁不同方向(光轴z和电轴x)振动的弹性柔顺常数存在的差别,导出压电梁弯曲振动的微分方程,并利用有限差分方法对几种典型的电极图形进行数值计算结果与结论 提出等效体力概念,给出了压电梁等效体力计算的一般公式,优选了振梁型传感器的电极图形。

Aim To provide the design parameter for the development of quartz angular rate sensor. Methods Based on piezoelectric theory and elastic mechanics theory, intrinsic differences between two vibrations in the x direction and the z direction were discussed for quartz crystal vibration beam, and the differential equation of the flexural vibration of piezoelectric beam was derived. Numerical calculations were performed for several typical electrode configurations. Results and Conclusion The concept of equivalent volume force was presented, and a general formula is given for it. Optimum electrode configurations were chosen, and the side ratio of the piezoelectric beam was also determined.