An exact solution for variable coefficients fourth-order wave equation using the Adomian method

Authors:
Hassan Haddadpour
Affiliations:
Department of Aerospace Engineering, Sharif University of Technology, Tehran, 11365-8639, Islamic Republic of Iran
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2006

Citing 3
Cited 3

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Applied Mathematics and Computation
Analytic treatment for variable coefficient fourth-order parabolic partial differential equations

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Exact solutions for variable coefficients fourth-order parabolic partial differential equations in higher-dimensional spaces

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Algorithmization and mechanization of the Cauchy problem associated with the plate equation

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Free vibration analysis of multiple-stepped beams by using Adomian decomposition method

Mathematical and Computer Modelling: An International Journal
Analysis of mixed finite element methods for fourth-order wave equations

Computers & Mathematics with Applications

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Abstract

This paper presents a novel approach for the analysis of a fourth-order parabolic equation dealing with vibration of beams by using the decomposition method. In this regard, a general approach based on the generalized Fourier series expansion is applied. The obtained analytic solution is simplified in terms of a given set of orthogonal basis functions. The result is compared with the classical modal analysis technique which is widely used in the field of structural dynamics. It is shown that the result of the decomposition method leads to an exact closed-form solution which is equivalent to the result obtained by the modal analysis method. Some examples are given to demonstrate the validity of the present study.