TY - JOUR
T1 - Homotopy perturbation for conservative Helmholtz-Duffing oscillators
AU - Leung, A. Y T
AU - Guo, Zhongjin
PY - 2009/8/7
Y1 - 2009/8/7
N2 - 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. © 2009 Elsevier Ltd. All rights reserved.
AB - 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. © 2009 Elsevier Ltd. All rights reserved.
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U2 - 10.1016/j.jsv.2009.02.045
DO - 10.1016/j.jsv.2009.02.045
M3 - RGC 21 - Publication in refereed journal
SN - 0022-460X
VL - 325
SP - 287
EP - 296
JO - Journal of Sound and Vibration
JF - Journal of Sound and Vibration
IS - 1-2
ER -