三维振动里兹法在变幅杆谐振特性分析中的应用研究

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振动与冲击 ›› 2012, Vol. 31 ›› Issue (18) : 163-168.

论文

三维振动里兹法在变幅杆谐振特性分析中的应用研究

秦慧斌1，2 吕明1 王时英1 李向鹏1

作者信息 +

Three dimensional vibration Ritz method application analysis in resonance of horns

Qin Hui-bin1, 2 Lv Ming1 Wang shi-ying1 LI Xiang-peng1

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文章历史 +

摘要

针对变幅杆振动分析的一维振动求解理论和齿轮超声加工研究现状，提出基于三维弹性动力学方程，利用能量变分原理，采用里兹法求解特征值的方法，统一了圆锥、圆截面指数形和悬链形变幅杆的扭转、纵向、弯曲振动的固有频率和振型求解方法；计算了不同直径比、长径比变幅杆的四位有效数字无量纲固有圆频率。设计加工了大、中、小截面指数形变幅杆，并利用锤击激励法做了模态实验。对其一维欧拉-伯努利、三维振动里兹数值法、有限单元法、实验模态法进行对比分析，结果表明：三维振动里兹数值法求解结果比一维振动求解理论准确，可以作为其他数值求解方法的验证标准；为其他非均匀截面变幅杆的振动特性分析提供了一种新的求解方法。

Abstract

The actuality of one dimensional vibration solution theory and gear ultrasonic machining was introduced. It presented a Ritz method in Energy-variational principle based on three dimensional elasticity kinetics equation. Three vibration mode such as longitudinal, bending and torsional vibration inherent frequencies and mode shapes for conical, exponential and catenary horns could be solved. Convergence to four-digit exactitude was demonstrated and tabulated for the three vibration modes of horns including different length diameter rations and diameter ratios of big end to small one. Three circle cross-section including large cross-section exponential ultrasonic horns were designed and machined. A structure modal experiment was carried out. Analytical solutions based on the three dimensional elastic vibration theory produce more accurate answers than ones that are based on the classical Euler-Bernoulli theory. Comparisons were made with the frequencies arising from 1 D classical Euler-Bernoulli beam theory to Three-dimensional elastic vibration Ritz method, finite elements method, and structure modal experiment. These data serve as benchmarks against which other approximate methods and other improved 1D classical Euler-Bernoulli beam theory may be tested. The present work proposes a new approach to vibration characteristics analysis of the acoustic horns with non uniform cross-section.

导出引用

秦慧斌;吕明王时英李向鹏. 三维振动里兹法在变幅杆谐振特性分析中的应用研究[J]. 振动与冲击, 2012, 31(18): 163-168

Qin Hui-bin; Lv Ming Wang shi-ying LI Xiang-peng . Three dimensional vibration Ritz method application analysis in resonance of horns[J]. Journal of Vibration and Shock, 2012, 31(18): 163-168