微分轉換於曲樑振動分析之研究

本文旨在探討應用微分轉換法求解曲樑異面振動問題。首先簡單介紹微分轉換法，其次推衍曲樑之統御方程式及邊界條件並取微分轉換，吾人可求得一組遞歸型式代數方程式，其次求解該方程式並取反微分轉換，即可求得曲樑之自然頻率及耦合振動模態。為印証本文所提方法之正確性，吾人以邊界條件為兩端固定及簡單支撐之曲樑為例求解自然頻率及耦合模態。最後將微分轉換法所求得的結果，與其他已發表研究結果比較其結果相當一致。

關鍵字

反微分轉換；微分轉換法；耦合振動模態；自然頻率

並列摘要

This study introduces a method using differential transforms to solve the vibration problem of curved beams. First, differential transform is briefly introduced. Second, deriving the governing equations and boundary conditions of curved beams vibration problem and taking differential transform of these equations and boundary conditions, a set of difference equations is derivied. Third, solving algebraic equations and taking inverse differential transform, we can determine any ith natural frequency and coupled vibration mode shape of curved beams. Finally, two vibration problems with fixed and simply-supported boundary conditions are given to illustrate the accuracy and efficiency of the present method.

並列關鍵字

Differential transform ； Inverse differential transform ； Coupled vibration mode shape ； Natural frequency

參考文獻

[1] Childamparam, P. and Leissa, A. W., “Vibrations of planar curved beams, Rings and Arches,” Applied Mechanics Reviews, Vol. 46, pp. 467-483, 1993.

[2] Auciello, N. M. and De Rosa, M. A. “Free vibrations of circular arches: A Review,” Journal of Sound and Vibration, Vol. 174, No. 4, pp. 433-458, 1994.

[3] Kawakami, M., Sakiyama, T., Matsuda, H., Morita, C., “In-plane and Out-of-plane free vibrations of curved beams with variable sections,” Journal of Sound and Vibration, Vol. 187, No. 3, pp. 381-401, 1995.

[4] Yang, Y.B., Wu, C.M., “Dynamic response of a horizontally curved beam subjected to vertical and horizontal moving loads,” Journal of Sound and Vibration, Vol. 242, No. 3, pp. 519-537, 2001.

circular curved beams resting on elastic foundation,” International Journal

國際替代計量

微分轉換於曲樑振動分析之研究

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