Li–He's modified homotopy perturbation method coupled with the energy method for the dropping shock response of a tangent nonlinear packaging system. Issue 2 (June 2021)

• Record Type: Journal Article
• Authors: Ji, Qiu-Ping; Wang, Jun; Lu, Li-Xin; Ge, Chang-Feng
• Is Part Of: Journal of low frequency noise, vibration, and active control. Volume 40:Issue 2(2021)
• Page Start: 675
• Page End: 682
• Publication Date: 2021-06
• Subjects: Tangent nonlinear differential equation -- Li–He's homotopy perturbation method -- energy method -- approximate solution; Vibration -- Periodicals; Noise -- Periodicals; Sound -- Periodicals; Damping (Mechanics) -- Periodicals; Damping (Mechanics); Noise; Sound; Vibration; Periodicals; 620.205
• DOI: 10.1177/1461348420914457
• Languages: English
• ISSNs: 1461-3484

Abstract

This paper couples Li–He's homotopy perturbation method with the energy method to obtain an approximate solution of a tangent nonlinear packaging system. A higher order homotopy equation is constructed by adopting the basic idea of the Li–He's homotopy perturbation method. The energy method is used to improve the maximal displacement and the frequency of the system to an ever higher accuracy. Comparison with the numerical solution obtained by the Runge–Kutta method shows that the shock responses of the system solved by the new method are more effective with a relative error of 0.15%.