A modification of He's variational approach using the least square method to nonlinear oscillators. Issue 3 (December 2019)

• Record Type: Journal Article
• Authors: Arif, Muhammad Shoaib; Nawaz, Yasir; Bibi, Mairaj; Fayyaz, Rabia; Naz, Mehvish
• Is Part Of: Journal of low frequency noise, vibration, and active control. Volume 38:Issue 3/4(2019)
• Page Start: 996
• Page End: 1007
• Publication Date: 2019-12
• Subjects: Variational method -- global error minimization -- nonlinear differential equations -- nonlinear oscillators; Vibration -- Periodicals; Noise -- Periodicals; Sound -- Periodicals; Damping (Mechanics) -- Periodicals; Damping (Mechanics); Noise; Sound; Vibration; Periodicals; 620.205
• DOI: 10.1177/1461348419828222
• Languages: English
• ISSNs: 1461-3484

Abstract

In this paper, we apply the global error minimization method to nonlinear oscillators with fractional terms for determining the first- and second-order approximate frequencies and solutions. The estimation problem is transformed into a minimization problem which leads to a simple yet precise scheme for finding the frequency of oscillation and the solution of the ordinary differential equation.