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基于Mindlin理论从声学应用角度,推导了中厚圆环在自由边界条件下的横向与径向位移及频率方程,并对频率方程进行数值求解,计算得到的频率与有限元模拟及试验测试结果基本相符,同时分析了厚圆环的几何参数和材料参数对频率的影响,结果表明当其他参数一定时,频率随厚度增加而增加,随内外半径的增加而减小。该结论为厚圆环及厚盘的弯曲振动辐射器的设计提供理论参考和频率调试依据。
Based on Mindlin theory, the transverse and radial displacement and frequency equations of medium-thick ring under free boundary condition are deduced from the angle of acoustic application. The frequency equation is numerically solved. The calculated frequency, finite element simulation and experimental test results are basically The results show that when the other parameters are constant, the frequency increases with the increase of the thickness and decreases with the increase of the inner and outer radii. The conclusion provides a theoretical reference and frequency debugging basis for the design of flexural vibration radiators for thick rings and thick plates.