Homotopy perturbation method coupled with the enhanced perturbation method. Issue 3 (December 2019)

• Record Type: Journal Article
• Authors: Li, Xiao-Xia; He, Chun-Hui
• Is Part Of: Journal of low frequency noise, vibration, and active control. Volume 38:Issue 3/4(2019)
• Page Start: 1399
• Page End: 1403
• Publication Date: 2019-12
• Subjects: Homotopy perturbation method -- Duffing equation -- frequency–amplitude relation -- periodic solution; Vibration -- Periodicals; Noise -- Periodicals; Sound -- Periodicals; Damping (Mechanics) -- Periodicals; Damping (Mechanics); Noise; Sound; Vibration; Periodicals; 620.205
• DOI: 10.1177/1461348418800554
• Languages: English
• ISSNs: 1461-3484

Abstract

The enhanced perturbation method is used to improve a governing equation to a higher order, followed by the classic perturbation method. This paper adopts the basic idea of the method to construct a homotopy equation with a higher order. The results show that this modification of the homotopy perturbation method leads to a very high accuracy of the obtained solution. Its solution process is elucidated by using Duffing oscillator as an example, and the obtained frequency is valid for all amplitudes from an extremely small value to infinity with a maximal error of 3.34%. The main merit of this higher order homotopy perturbation method is that the obtained frequency is valid for the whole solution domain.