An innovative eigenvalue problem solver for free vibration of Euler-Bernoulli beam by using the Adomian decomposition method

Authors:
Hsin-Yi Lai;Jung-Chang Hsu;Cha'o-Kuang Chen
Affiliations:
Department of Mechanical Engineering, National Cheng-Kung University, No. 1, University Road, Tainan 701, Taiwan, ROC;Department of Mechanical Engineering, National Cheng-Kung University, No. 1, University Road, Tainan 701, Taiwan, ROC;Department of Mechanical Engineering, National Cheng-Kung University, No. 1, University Road, Tainan 701, Taiwan, ROC
Venue:
Computers & Mathematics with Applications
Year:
2008

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Abstract

This paper deals with free vibration problems of Euler-Bernoulli beam under various supporting conditions. The technique we have used is based on applying the Adomian decomposition method (ADM) to our vibration problems. Doing some simple mathematical operations on the method, we can obtain ith natural frequencies and mode shapes one at a time. The computed results agree well with those analytical and numerical results given in the literature. These results indicate that the present analysis is accurate, and provides a unified and systematic procedure which is simple and more straightforward than the other modal analysis.