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Computing Simulation of the Generalized Duffing Oscillator Basedon EBM and MHPM

Azimi A., Azimi M.

Mechanics and Mechanical Engineering

2016

Vol. 20, nr 4

595--604

This paper is concerned with analytical approximate solutions, to the generalized Duffing oscillation. Modified Homotopy Perturbation Method (MHPM) and Energy Balance Method (EBM) are applied to solve nonlinear equation and consequently the relationship between the natural frequency and the initial amplitude is obtained in an analytical form. The general solution can be used to yield the relationship between amplitude and frequency in different strengths of nonlinearity. To verify the accuracy of the present approach, illustrative examples are provided and compared with exact solutions. The procedure yields rapid convergence with respect to the exact solution obtained by numerical integration.