Transverse vibration of a rotating twisted Timoshenko beams under axial loading using differential transform |
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Authors: | Chao Kuang Chen Shing Huei Ho |
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Affiliation: | a Department of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan, ROC;b Department of Mechanical Engineering, Kung Shan Institute of Technology, Tainan, Taiwan, ROC |
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Abstract: | This study introduces the concept of a differential transform to solve the free vibration problems of a rotating twisted Timoshenko beam under axial loading. First, the concept of differential transform is briefly introduced. Second, taking a differential transform of a Timoshenko beam vibration problem, a set of difference equations is derived. Performing some simple algebraic operations on these equations, we can determine the jth natural-frequency, the closed form series solution of the jth mode shape. Finally, three cases—twist, axial force and rotation—are investigated to illustrate the accuracy and efficiency of the present method. |
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Keywords: | Differential transform Differential inverse transform Recursive procedure Natural frequency Coupled mode shape |
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