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Research Article Open access CC BY 4.0

Analyzing of Nonlinear Generalized Duffing Oscillators Using the Equivalent Linearization Method with a Weighted Averaging

D. V. Hieu, N. Q. Hai

Asian Research Journal of Mathematics · pp. 1–14 · Published 14 Apr 2018

10.9734/ARJOM/2018/40684

Abstract

The generalized Duffing oscillator is investigated in this paper by using the Equivalent Linearization method with a weighted averaging. Applying of the Equivalent Linearization method in which the averaging value is calculated in a new way called the weighted averaging value by introducing a weighted coefficient function, the amplitude-frequency relationship of the oscillator is obtained in a closed-form. The obtained solutions have been compared with approximate analytical solutions, exact solutions and numerical solutions. Comparisons show the reliability of the present solutions.

Equivalent linearization method weighted averaging generalized Duffing nonlinear oscillator.

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