复合弯曲超声换能器边缘自由薄板多波节振动分析

Analysis of vibration of free edged thin plate with multi nodal circles applied to compound flexural ultrasonic transducer

本文讨论了边缘自由条件下轴对称薄板弯曲振动时的频率方程及其求解，并给出了前９个根（泊松比σ＝０．３３）的精确值和９种振动模式的波节圆半径的计算值。对薄板的高次弯曲振动模式的分析及大圆盘、多波节复合弯曲超声换能器的设计提供了理论计算依据。

In this paper, the frequency equation of axisymmetric flexural vibrating free edged thin plate and it's solving process are discussed, it's nine roots (Poisson's ratio σ=0.33)and calculating value of nodal circles' of nine kinds vibrating modes are given. These provide theoretical calculation basis for analysis of high mode flexural vibration of plate and design of big round plate and multi nodal compound flexural ultrasonic transducer.