任意變化厚度之旋轉圓盤振動分析與最佳形狀設計

Vibration Analysis and Shape Optimization of Spinning Disks of Arbitrary Thickness

呂哲匡(Jer-Kuang Lu)

指導教授 ： 張英俊

大同大學/工程學院/機械工程學系所/碩士(2006年)

摘要

本文主要探討的部分為以薄板理論研究任意變化厚度之等向性圓盤的應力分布及臨界轉速。以不同之內外徑比及厚度比評估臨界轉速，結果顯示較大的內外徑比或厚度參數均能有效地增加在較低模態下的臨界轉速。
將遺傳演算法 (G.A. ) 與轉移矩陣法結合來分析要達到應力均勻分布和能提升旋轉圓盤之臨界轉速的形狀設計，數值分析結果得出應力均勻分布之例子顯示內外徑比下降則厚度分布變化劇烈。在高轉速的圓盤之厚度分布會比低轉速的分布較陡峭，高轉速的內徑之厚度會較低轉速的高。

關鍵字

振動 ； 等向性圓盤 ； 厚度 ； 遺傳演算法

並列摘要

In this study, the stress distribution and critical speed of rotating isotropic disk with arbitrary thickness are investigated based on the thin plate theory. The critical speed is evaluated for different values of radius ratio and thickness ratio. The results show that increasing the values of ratio of radii and thickness parameter can effectively increase the critical speed of the plate for a lower order mode.
By incorporating Genetic algorithm (G.A ) method and transfer matrix
analysis, the shape design of rotating disks for uniform stress distribution
and enhancing critical speed has also been implemended. Numerical
results show that for the case of uniform stress, the thickness distribution of
the disk shows larger variation as the radius ratio is decreased.
The thickness distribution of the disk with a higher rotating speed is more precipitous than those at lower rotating speed. The thickness of inner edge for the disk at high rotating speed is thicker than those at low rotating speed.

並列關鍵字

Vibration ； Isotropic annular plate ； Thickness ； Genetic algorithm

參考文獻

[1] G. G. Adams 1987 Int. J. Mech. Sci 129(8), 525-531. Critical Speeds for a Flexible Spinning Disk.

[2] S. Chonan 1987 Journal of Applied Mechanics 54, 967-968. On the Critical Speed of a Rotating Circular Plate.

[4] S. K. Sinha 1988 ASME, Transactions, Journal of Vibrations, Acoustics, Stress, and Reliability in Design 110, 507-514. On Free Vibrations of a Thin Spinning Disk Stiffened with an Outer Reinforcing Ring.

[5] S. M. Yang 1993 Journal of vibrations and acoustics 115, 159-164. Vibration of a Spinning Annular Disk with Coupled Rigid-Body Motion.

[6] A. Phylactopoulos and G. G. Adams 1999 ASME, Journal of Vibration and Acoustics 121(7), 273-279. Transverse Vibration of a Rectangularly Orthotropic Spinning Disk, Part 1: Formulation and Free Vibration.