Comparison of Adomian Decomposition Method and Differential Transformation Method for Vibration Problems of Euler-Bernoulli Beam

Abstract:

In this paper, we compare the Differential transformation method and Adomian decomposition method to solve Euler-Bernoulli Beam vibration problems. The natural frequencies and mode shapes of the clamped-free uniform Euler-Bernoulli equation are calculated using the two methods. The Adomian decomposition method avoids the difficulties and massive computational work inherent in Differential transformation method by determining the very rapidly convergent analytic solutions directly. We found the solution between the two methods to be quite close. According to calculation of eigenvalues, natural frequencies and mode shapes, we compare the convergence of Differential transformation method and Adomian decomposition method. The two methods can be alternative ways to solve linear and nonlinear higher-order initial value problems.

• Periodical: Applied Mechanics and Materials (Volumes 157-158)
• Pages: 476-483
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.157-158.476
• Online since: February 2012
• Authors: Zhifeng Liu, Chun Hua Guo, Li Gang Cai, Wen Tong Yang, Zhi Min Zhang
• Keywords: Adomian Decomposition Method, Clamped-Free, Differential Transformation Method, Frequency, Mode, Nonlinear, Uniform Euler-Bernoulli Beam

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