上海交通大学学报

上海交通大学学报（自然版） ›› 2011, Vol. 45 ›› Issue (06): 940-944.

• 数学 • 上一篇    

n次幂变厚度环形超声聚能器径向振动特性

刘世清1,苏超1,姚晔2   

  1. （1．浙江师范大学 应用声学研究所,浙江 金华 321004；2．上海交通大学 机械与动力工程学院,上海 200240）
  • 收稿日期:2010-05-10 出版日期:2011-06-29 发布日期:2011-06-29
  • 基金资助:

    国家自然科学基金资助项目(11074222)，浙江师范大学硕士论文培优项目(ZC316011021)

Radial Vibration Characteristics of an Annular Ultrasonic Concentrator with n-th Power Thickness Variations

 LIU  Shi-Qing-1, SU  Chao-1, YAO  Ye-2   

  1. (1. Applied Acoustic Institiute, Zhejiang Normal University, Jinhua 321004, Zhejiang, China; 2. School of Mechanical Engineering, Shanghai Jiaotong University, Shanghai 200240, China)
  • Received:2010-05-10 Online:2011-06-29 Published:2011-06-29

摘要： 对剖面厚度按n次幂函数变化的环形超声聚能器的径向振动特性进行研究.基于机电类比原理，推导出环形聚能器的径向振动机电等效电路及其径向共振频率方程，给出了聚能器的位移振幅放大系数表达式，探讨了第1、2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2阶共振频率随半径比变化存在1个极小值.此外，振幅放大系数随幂次n增高而增大，第2阶共振具有更高的振幅放大系数.有限元仿真结果与理论相吻合.

关键词: 环形聚能器, 振幅放大系数, 等效电路, 频率方程

Abstract: The radial vibration of an annular ultrasonic concentrator with nth power thickness variation was studied. Based on the electromechanical analogy, the radial equivalent circuit and the frequency equation were derived. The displacement amplitude magnification coefficient of the concentrator was obtained. The relationships between the resonance frequency, the radial displacement amplitude magnification coefficient of the concentrator at the first and second order vibration modal and the radius ratio of it were analyzed. By numerical calculation, it is shown that the radial fundamental frequency of the concentrator decreases as the radius ratio increases. While a minimum of the second order resonance frequency appears when the radius ratio of the annular concentrator increases. Moreover, the displacement amplitude magnification coefficient of the concentrator increases as the power of nth increases, and the amplitude magnification coefficient at the second order resonance is much greater than that of the first order resonance. It is illustrated that the theoretical results are in good agreement with the FEM simulations.

Key words: annular concentrator, amplitude magnification coefficient, equivalent circuit, frequency equation

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