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.


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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