Application of Homotopy Perturbation Method for Harmonically Forced Duffing Systems
In this paper, He’s homotopy perturbation method (HPM) is applied to solve harmonically forced Duffing systems. Non-resonance of an undamped Duffing system and the primary resonance of a damped Duffing system are studied. In the former case, the first-order analytical approximations to the system’s natural frequency and periodic solution are derived by HPM, which agree well with the numerical solutions. In the latter case, based on HPM, the first-order approximate solution and the frequency-amplitude curves of the system are acquired. The results reveal that HPM is an effective technique to the forced Duffing systems.
X. M. Zhang et al., "Application of Homotopy Perturbation Method for Harmonically Forced Duffing Systems", Applied Mechanics and Materials, Vols. 110-116, pp. 2277-2283, 2012