薄圆桶压电振子的弯曲振动分析

Analysis of the piezoelectric disk resonator with barrel shell in flexural vibration

薄圆桶压电振子是薄金属圆桶底部粘合压电陶瓷圆片的振动元件。文章利用瑞利—里兹法,采用弹性边界约束条件,对薄圆桶压电振子的振动特性进行理论分析,推导得到压电振子振动频率方程,通过数值计算分析支撑结构对压电振子频率的影响,为该类传感器的研制提供设计依据。经分析计算,当压电振子中陶瓷圆片结构确定时,振子的谐振频率随支撑结构厚度的增加、半径的减小而增大。其中当金属底面厚度与振子总厚度之比在0.5-0.75之间时,振子谐振频率变化缓慢,当两者厚度比超过0.75后,谐振频率迅速增高;而当压电圆片与支撑结构半径比在0.4-0.9之间变化时,振子谐振频率随两者半径比的增大而增加,变化斜率也略有增大。

A ceramic disk plastered at the bottom of the metal shell constitutes the piezoelectric disk resonator with barrel shell. Vibration frequency of the resonator is deduced by Rayleigh-Ritz energy equation and elastic boundary conditions. Influence of the resonator structure on the resonant frequency is analyzed.The result shows that the resonant frequency !f＂increases with the raise of thickness ratio !α＂and radius ratio !β＂. The frequency changes little during α is the range of 0.5-0.75, but the frequency is rising rapidly when α is bigger than 0.75. The rake ratio of f/β increases a bit with the raise of β in the range of 0.4-0.9.The analysis result could be the reference about the design and manufacture of the piezoelectric disk resonator.