幂函数剖面环形超声聚能器的振动特性及其仿真分析

An annular ultrasonic concentrator with power function profile and FEM simulation for its radial vibration

对剖面厚度按幂函数变化的环形超声聚能器的径向振动特性进行了理论分析.基于机电类比原理,推导出环形聚能器径向振动的机电等效电路及其共振频率方程,给出了其位移振幅放大系数的表达式;探讨了聚能器第一、第二阶共振聚能器位移振幅放大系数及共振频率与其半径比的关系.计算表明:聚能器基频随半径比增大而降低;而第二阶共振频率随半径比变化存在一极小值.此外,振幅放大系数随幂次n增高而增大;第二阶共振具有更高的振幅放大系数.有限元仿真结果与理论吻合.

The radial vibration of annular ultrasonic concentrator with power function profile was studied.Based on the electromechanical analogy,the radial equivalent circuit and the frequency equation were derived.The displacement amplitude magnification coefficient of the concentrator was obtained.The relationships between resonance frequency,radial displacement amplitude magnification coefficient of the concentrator at the first and second order vibration modal and their radii ratio were analyzed.By numerical calculation,it was showed that the radial fundamental frequency of the concentrator decreased as the radius ratio increased.While a minimum of the second order resonance frequency appeared when the radii ratio of the annular concentrator increased.Moreover,the displacement amplitude magnification coefficient of the concentrator increased as the power of n increased,and the amplitude magnification coefficient at the second order resonance was much greater than that of the first order resonance.The FEM simulations were illustrated good agreement with the theoretical results.