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An approximation solution for one-dimensional weakly nonlinear oscillations. (English) Zbl 1079.34028

Summary: A combination of some methods: a perturbation method, variational iteration method, method of variation of constants and the averaging method is presented to establish an approximate solution of one-degree-of-freedom weakly nonlinear system. This method is a powerful tool for determination of general or periodic solutions of a nonlinear equation of motion. We distinguish the “nonresonance” and “resonance” case. These analytical research are verified with numerical examples and a very good agreement is found, which shows the applicability of the method.

MSC:

34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
34C29 Averaging method for ordinary differential equations
34E05 Asymptotic expansions of solutions to ordinary differential equations
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[1] DOI: 10.1016/0022-460X(85)90534-6 · doi:10.1016/0022-460X(85)90534-6
[2] Math Anal J., Appl. 135 pp 501– (1998)
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