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Study on Free Oscillations of Systems with Even Nonlinearities by Means of the Method of Multiple Scales

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Abstract:

An analytical technique, namely the method of multiple scales, is applied to solve the differential equations of free oscillations with even nonlinearities in a mass-spring system. Unlike other perturbation methods, the method of multiple scales is effective in determining the transient response as well as determining the approximation to the frequency of the nonlinear system. In this paper, the periodic solutions of the even nonlinear differential equations have been obtained by using the method of multiple scales. Compared with the numerical examples, the approximate solutions are in good agreement with exact solutions. The numerical and analytical solutions have clearly shown that there exists the so-called drift phenomenon in the free oscillations of systems with even nonlinearities without any external excitation.

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Periodical:

Applied Mechanics and Materials (Volumes 10-12)

Pages:

193-197

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.10-12.193

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Online since:

December 2007

Authors:

J.M. Wen, Z.C. Cao

Keywords:

Analytical Solution, Free Oscillations, Method of Multiple Scales, Numerical Solution, Systems with Even Nonlinearities

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© 2008 Trans Tech Publications Ltd. All Rights Reserved

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