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幂函数型环形聚能器径向振动的等效电路
引用本文:许龙,李伟东.幂函数型环形聚能器径向振动的等效电路[J].声学学报,2019,44(5):826-833.
作者姓名:许龙  李伟东
作者单位:中国计量大学 物理系 杭州 310018
基金项目:浙江省自然科学基金项目(LY16A040006)国家自然科学基金项目(11574277)资助
摘    要:基于机电类比原理和变厚度薄圆环的平面应力方程,推导了幂函数型环形聚能器径向振动的等效电路、共振频率方程和位移放大系数。讨论了第一、二阶径向共振频率及相应的位移放大系数随圆环半径比的变化关系。结果表明,幂函数型环形聚能器径向振动的等效电路是一种非互易二端口等效网络;一阶和二阶共振频率随圆环内外半径比的增大而增大;一阶径向共振模式下位移放大系数随圆环半径比的增大先降低后升高,二阶径向共振模式下位移放大系数随圆环半径比的增大而降低,但二阶时的位移放大系数整体大于一阶,因此二阶径向共振模式具有更好的径向振动性能。用COMSOL有限元软件对解析理论分析结果进行了验证,仿真模拟结果与解析理论符合良好。根据幂函数型环形聚能器的等效电路模型,进一步设计了一种压电环形换能器,计算了第一、二阶径向共振频率、反共振频率及有效机电耦合系数,通过与COMSOL有限元软件模拟结果对比,符合良好。本文研究结果为幂函数型环形聚能器及压电环形换能器的工程应用提供了简明设计理论,文中研究结论可作为一种径向超声切割刀在超声工程中获得重要应用。 

关 键 词:径向振动    等效电路    环形聚能器    有限元分析
收稿时间:2017-09-12

The equivalent circuit of the annular plate concentrator with power function cross-section in radial vibration
Institution:Department of Physics, China JiLiang University, Hangzhou 310018
Abstract:Based on the principle of electro-mechanical analogy and the plane stress equation of a thin annular plate with thickness variation,the equivalent circuit,the resonance frequency equation and the displacement amplitude magnification coefficient of the annular plate concentrator with power function cross-section in radial vibration are derived.The relationships between the radius ratio and the radial resonance frequency and the displacement amplitude magnification coefficient at the first and second order resonance modes of the concentrator are analyzed.The result shows that the equivalent circuit of the annular plate concentrator with power function cross-section in radial vibration is a novel non-reciprocal two-port equivalent network.The first and second resonance frequencies of the concentrator increase as its radius ratio increases;the displacement amplitude magnification coefficient decreases firstly and then increases as the radius ratio increases at the first order radial resonance mode;the displacement amplitude magnification coefficient increases as the radius ratio increases at the second order radial resonance mode.The displacement amplification magnification coefficient at the second order resonance mode is larger than that of the first order resonance mode,so the second order radial resonance mode has better radial vibration performance.The theory results are confirmed by the finite element method(COMSOL Multiphysics).According to the equivalent circuit model of the annular plate concentrator with power function cross-section,a piezoelectric ceramic annular transducer is designed;the first and second order radial resonance,anti-resonance frequency and the effective electro-mechanical coupling coefficient of the piezoelectric transducer are calculated.The results are in good agreement with the finite element method.It provides a concise design theory for the engineering application of the annular plate concentrator with power function cross-section and the related piezoelectric transducer.It is expected to be used as a radial ultrasonic cutting knife used in ultrasonic engineering. 
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