Homotopy perturbation for conservative Helmholtz–Duffing oscillators
Author(s)
Author(s)
Guo, Z.
Date Issued
2009
Publisher
Elsevier
Journal
Journal of Sound and Vibration
Volume
325
Issue
1-2
Start page
287
End page
296
Abstract
The approximate periodic solutions of the Helmholtz–Duffing oscillator are obtained by homotopy perturbation. The Helmholtz–Duffing oscillator becomes a Duffing oscillator when the homotopy parameter degenerates to one and a Helmholtz oscillator when it is zero. Since the behaviors of the solutions in the positive and negative directions are quite different, the asymmetric equation is separated into two auxiliary equations. The auxiliary equations are solved by homotopy perturbation method. A new analytical period for the Helmholtz–Duffing equation is derived. The resulting second-order approximate periodic solutions are compared to the analytical solutions using numerical integration with improved accuracy over some existing methods. Thus, the homotopy perturbation is very effective for the asymmetric nonlinear oscillators.
SFU Affiliated Publication
No
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