Application the Adomian Decomposition Method to the Dynamic Response Analysis of Cracked Beam under Moving Load
Keywords:
Adomian decomposition method, Euler-Bernoulli beam, Cracked beam, moving load, mode shape functions, eigenvalue equationAbstract
In this article, the Adomian method of decomposition (ADM) is used to examine the vibration of a simply supported cracked beam (SSCB) under a moving load based on the Euler Bernoulli hypothesis. the system modelled as two segments of the beam are to be connected by a massless elastic rotational spring. Bearing in mind each segment of a cracked beam a substructure that can be modeled using ADM. ADM derives for the first time on the basis of kinematic conditions and boundary conditions the characteristic / eigenvalue equation and mode shape functions of the cracked beam under a moving load. The results obtained from ADM are compared to the results obtained from the method of finite elements (FEM). ADM results show remarkable superiority compared to FEM.
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