An effective modification of He's variational approach to a nonlinear oscillator. Issue 3 (December 2019)

• Record Type: Journal Article
• Authors: Nawaz, Yasir; Arif, Muhammad Shoaib; Bibi, Mairaj; Naz, Mehvish; Fayyaz, Rabia
• Is Part Of: Journal of low frequency noise, vibration, and active control. Volume 38:Issue 3/4(2019)
• Page Start: 1013
• Page End: 1022
• Publication Date: 2019-12
• Subjects: Variational approach -- nonlinear oscillators -- analytical approximation methods; Vibration -- Periodicals; Noise -- Periodicals; Sound -- Periodicals; Damping (Mechanics) -- Periodicals; Damping (Mechanics); Noise; Sound; Vibration; Periodicals; 620.205
• DOI: 10.1177/1461348419829372
• Languages: English
• ISSNs: 1461-3484

Abstract

This paper is concerned with the application of the variational principle to nonlinear oscillators with fractional power. In the proposed approach, high-order trial solutions are assumed with unknown parameters that are estimated using conditions by the variational theory. To perform integration in the proposed approach, linearization of the nonlinear term is carried out for simple calculation. The proposed approach delivered an estimate of the oscillator frequency with a relative error as small as 0.009%.