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THE GALERKIN METHOD FOR INITIAL VALUE PROBLEMS BASED ON THE PRINCIPLE OF TOTAL VIRTUAL ACTION

✍ Scribed by G. Chen; H. Du

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 213 KB
Volume: 203
Category: Article
ISSN: 0022-460X
DOI: 10.1006/jsvi.1996.0852

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✦ Synopsis

In this paper is presented the derivation of the unconstrained variational statement for initial value problems from the viewpoint of the Principle of Total Virtual Action. Based on the hybrid form of the variational equation, both the Galerkin and the recurrent-Galerkin procedures are developed. They are used to obtain approximate analytical/semi-analytical solutions. Linear and non-linear vibration problems are used to demonstrate the applications. Comparison between the results obtained with initial conditions unconstrained and those with initial conditions constrained is made. Different weighting functions are tried out to confirm the validity of the ''hybrid'' form of the unconstrained variational statement.

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