厚圆盘弯曲振动研究

当厚跨比大于五分之一时,研究板弯曲振动中的剪切应力及由此引起的剪切、扭转变形等就不能忽略,经典的薄板理论将失效.从声学应用的角度,基于Mindlin板理论,本文推导了厚圆盘弯曲振动径向位移和横向位移的解析表达式,并得到了自由、简支、固定边界条件下的频率方程.解析方法计算得到的前几阶振型对应的频率与有限元方法计算的结果基本相符,与实验测试结果基本一致.本文的结果对厚圆盘弯曲振动辐射器的设计提供了理论参考. 关键词： 厚圆盘 弯曲振动 频率方程

Analysis of flexural vibration thick disk

The flexural vibration of thick disk is studied in this paper. The general solutions of radial displacement and transverse displacement for flexural vibration thick disk under the Mindlin theory are derived. The resonance frequency equations are derived when the boundary conditions are free, simply supported and clamped, and The results obtained from the analyticae method are in good agreement with those from the finite element method and also with the experimental results. These results can serve as reference for the design of flexural vibration thick disk radiator.