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A non-linear seales method for strongly non-linear oscillators

✍ Scribed by Z. Xu; Y. K. Cheung

Publisher
Springer Netherlands
Year
1995
Tongue
English
Weight
620 KB
Volume
7
Category
Article
ISSN
0924-090X

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✦ Synopsis

A non-linear scales method is presented for the analysis of strongly non-linear oscillators of the form Y: + g(x) = ef (x, d:), where g(x) is an arbitrary non-linear function of the displacement x. We assumed that x(t,~) x0(~,,7) + m-, m T~ = ~,~=~ e'~xn(~) + O(e'~), where d~/dt = ~,~=1 e'~R~(~) , d~7/dt = ~,~=0 e'~S~( ~, ~)

, and R~, S,~ are to be determined in the course of the analysis. This method is suitable for the systems with even non-linearities as well as with odd non-linearities. It can be viewed as a generalization of the two-variable expansion procedure. Using the present method we obtained a modified Krylov-Bogoliubov method. Four numerical examples are presented which served to demonstrate the effectiveness of the present method.

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