Three dimensional vibration Ritz method application analysis in resonance of horns

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Journal of Vibration and Shock ›› 2012, Vol. 31 ›› Issue (18) : 163-168.

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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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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.

Key words

Three dimensional elastic vibration / Ritz method / Acoustic horn / Resonant frequency

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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