本研究探討樑強化旋轉圓板系統具失序(disorder)或失調(mistune)之振動特性分析。文中首先由能量準則，推導出旋轉樑與旋轉圓板承受簡諧線負荷之運動方程式，續由此方程式進行自由與強迫振動分析，復利用接納法理論(receptance theory)，結合旋轉樑與圓板，以求得樑強化旋轉圓板系統具失序或失調之固有頻率及模態方程式。
文中考慮樑接於圓板單側，數值求解添加不同根數樑圓板系統於完美、具一角度失序或一剛性失調等三種情況下結合，並分析系統之固有頻率及模態變化，最後進行系統參數效應分析。經數值結果得知，等距添加適當數目強化樑可強化圓板的結構，但當系統有輕度角度失序時，則易造成固有頻率的分歧;當系統具剛性失調時，系統頻率則隨著失調因子的正或負而上升或下降。文中所得結果均以合理物理觀點解釋之。

The purpose of this paper is to study the vibration characteristic of a spinning annular plate with disordered of mistuned beam-stiffeners. First, via the principle of energy, we derive the equations of motion of the rotating beam and plate. Galerkin’s method is then employed to discretize the equation. The receptance method follows to join the rotating beam and plate, and yield the natural frequencies and mode shapes.
　　In this paper the beams reinforcement one-side on the plate. Numerical results for three combine situation, perfect, with disordered or mistuned. In the same time, analyze the system’s change of natural frequencies and mode shape. Finally, parametric studies of systems are conducted. The results show that adequate number of beams do stiffen the spinning plate. But a mistuned beam has caused frequencies bifurcation. A mistuned beam has caused frequencies increase and decrease when mistuned error was raised or downed. All the results are well interpreted and illustrated from physical viewpoint.

參考文獻

[1]Bishop, R. E. D. and Johnson, D. C., The Mechanics of Vibration, Cambridge University Press, London(1960).
[2]Lamb, H. and Southwell, R. V., “The Vibration of a Spinning Disk,” Proceedings of the Royal Society, London, 99, pp. 272-280(1921).
[3]Southwell, R. V., “On the Free Transverse Vibration of a Uniform Circular Disk at Its Center and on the Effects of Rotating,” Proceedings of the Royal Society, London, 101, pp. 133-153(1921).
[4]Vogel, S. M. and Skinner, D. W., “Natural Frequencies of Transversely Vibrating Uniform Annular Plates,” ASME Journal of Applied Mechanics, 32, pp. 926-931(1965).
[5]Mote, C. D. Jr., “Free Vibrations of Initially Stressed Circular Disks,” ASME Journal of Engineering for Industry, 87(2), pp. 258-264(1965).
[6]Chi, C., “Modes of Vibration in a Circular Plate with Three Simple Support Points,” AIAA Journal, 10(2), pp. 142-147(1965).
[7]Iwan, W. D. and Moeller, T. L., “The Stability of a Spinning Elastic Disk with a Transverse Load System,” ASME Journal of Applied Mechanics, 43, pp. 485-490(1976).
[8]Good, J. K. and Lowery, R. L., “Finite Element Modeling of the Free Vibration of a Read/Write Head Floppy Disk System,” ASME Journal of Vibrations, Acoustics, Stress and Reliability in Design, 107(3), pp. 329-333(1985).
[9]Hutton, S. G., Chonan, S. and Lehmann, B. F., Dynamic Response of a
Guided Circular Saw, Journal of Sound and Vibration, 112(3), pp. 527-539(1987).
[10]Huang, S. C., and Yu, S. C., “On the Free Vibration of Rotating Annular Plates Elastically Restrained at Discrete Locations,” Journal of the Chinese Society of Mechanical Engineers, 11(6), pp. 488-498(1990).
[11]Huang, S. C. and Hsu, B. S., “Theory of Receptance Applied to Modal Analysis of a Spinning Disk with Interior Multi-Point Supports,” ASME Journal of Vibration and Acoustics, 114, pp. 468-476(1992).
[12]Huang, S. C. and Hsu, B. S., “Vibrations of a Spinning Annular Plate
with Multi-Circular Line Guides,” Journal of Sound and Vibration, 164(3), pp. 535-547(1993).
[13]Huang, S. C. and Wu, C. H., “Vibration of a Rotating Plate with Radial Ribs Reinforcement,” Journal of the Chinese Society of Mechanical Engineers, 17(4), pp. 323-333(1996).
[14]Pierre, C. and Dowell, E. H., “Localization of Vibrations by Structural Irregularity,” Journal of Sound and Vibration, 114(3), pp. 549-564(1987).
[15]Leissa, A. W., “On a Curve Veering Aberration,” Journal of Applied Mathematics and Physics, 25, pp. 99-111(1974).
[16]Ulsoy, A. G., Pierre, C. and Ulsoy, C., “Vibration Localization in Rotating Shafts, part 1 : Theory,” Transaction of the ASME, Journal of Vibration and Acoustics, 120, pp. 138-148 (1998).
[17]Huang, S. C. and Chiu, Y. J., “The Influence on Rotor Coupling Vibration and Stability Due to a Mistuned Blade’s Staggle Angle,” Shock and Vibration, submitted.