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Comparative vibration analysis of a parametrically nonlinear excited oscillator using HPM and numerical method. (English) Zbl 1152.70012

Summary: We present an analytical investigation of the vibrations of a parametrically excited oscillator with strong cubic negative nonlinearity based on Mathieu-Duffing equation. The analytic investigation is conducted by using He’s homotopy-perturbation method (HPM). The Runge-Kutta algorithm is used to solve the governing equation numerically. To demonstrate the validity of the proposed method, the approximate analytical solution is compared with numerical solution. Afterward, the effects of variation of parameters on the accuracy of homotopy-perturbation method are studied.

MSC:

70K28 Parametric resonances for nonlinear problems in mechanics
70K60 General perturbation schemes for nonlinear problems in mechanics
70-08 Computational methods for problems pertaining to mechanics of particles and systems
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