弯曲振动薄圆盘的共振频率和等效电路参数研究

摘要

The electro-mechanical equivalent circuit is the most common method of analyzing and designing composite transducers. How-ever, for the thin disk, because of the complexity of flexural vibration, equivalent lumped parameters are difficult to obtain, and so this method is rarely used. From the point of equivalent view of the distributed parameter system and lumped parameter system, according to the kinetic energy equal principle and the potential energy equal principle in this paper, we give the lumped parameter equivalent mass and equivalent elasticity coefficient of the flexural vibration, and the resonance frequency equations as well. The results from the analytical method are in good agreement with those from the finite element method. Finally, the equivalent circuit of lumped parameter model of the thin disk in analyzing the composite vibration system is given. These results can serve as a reference for designing flexural vibration composite transducers.%　　机电等效电路是分析复合换能器常用的一种解析方法，但对薄圆盘而言，由于弯曲振动的复杂性，其等效集中参数很难获得，该方法很少被应用。本文从分布参数系统与集中参数系统等效角度，根据动能相等原则和势能相等原则，给出了弯曲振动薄圆盘的集中参数：等效质量和等效弹性系数，得到了共振频率方程，并用ATILA软件模拟了其振动分布情况，可以看出解析结果与数值结果趋于一致。最后给出了分析复合振动系统时薄圆盘集中参数模型的等效电路。本文的结果对弯曲振动复合换能器的设计提供了理论参考。