Three dimensional vibration solving for axisymmetric vibration frequency of annular disk using Ritz method

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Journal of Vibration and Shock ›› 2013, Vol. 32 ›› Issue (17) : 52-58.

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Three dimensional vibration solving for axisymmetric vibration frequency of annular disk using Ritz method

QIN Hui-bin1, 2 LÜ Ming1 WANG Shi-ying1

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Abstract

It presented a Ritz numerical value method in Energy-variational principle based on three dimensional elasticity kinetics equation in allusion to the design of vibration system in gear ultrasonic shaving and honing. Axisymmetric free vibration such as transverse flexural and radial vibration inherent frequencies and mode shapes for annular disk with non-uniform thickness cross section could be solved. Convergence to four-digit frequency coefficient was demonstrated and tabulated for the two modes of annular disks including different thickness diameter rations, hole diameter ratios, material poison coefficient and thickness variety coefficient along radial direction. Furthermore, the rule of vibration frequency coefficient change was brought out. Annular disks with different thickness diameter rations and tapered thickness along radial direction were designed and machined. A structure modal experiment was carried out. Comparisons were made with the frequencies arising from three-dimensional elastic vibration Ritz method to Mindlin plate theory, finite elements method, and structure modal experiment. These data can serve as benchmarks against which other approximate methods. The present work proposes a new approach to vibration characteristics analysis of the annular disks with non uniform cross-section. The conclusion has certain theoretical guidance and engineering application significance to design the vibration system of ultrasonic gear machining.

Key words

Annular disk / Annular disk with non-uniform thickness cross section / Transverse flexural vibration / Radialvibration / Three dimensional elastic vibration Ritz method

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QIN Hui-bin; LÜMing WANG Shi-ying . Three dimensional vibration solving for axisymmetric vibration frequency of annular disk using Ritz method[J]. Journal of Vibration and Shock, 2013, 32(17): 52-58