Variational iteration algorithm I with an auxiliary parameter for the solution of differential equations of motion for simple and damped mass–spring systems. (January 2020)

• Record Type: Journal Article
• Authors: Ahmad, Hijaz; Khan, Tufail A
• Is Part Of: Noise & vibration worldwide. Volume 51:Number 1/2(2020)
• Page Start: 12
• Page End: 20
• Publication Date: 2020-01
• Subjects: Variational iteration algorithm I -- variational iteration algorithm I with an auxiliary parameter -- vibration problems -- transverse vibration -- mass–spring system; Noise control -- Periodicals; Damping (Mechanics) -- Periodicals; Soundproofing -- Periodicals; Damping (Mechanics); Noise control; Soundproofing; Periodicals; 620.205
• DOI: 10.1177/0957456519889958
• Languages: English
• ISSNs: 0957-4565

Abstract

In this article, variational iteration algorithm I with an auxiliary parameter is used for simple and damped mass–spring systems that undergo forced vibrations and transverse vibration of uniform and variable beams with simply supported analytical treatment. In addition, common vibration problems are classified and the values of Lagrange multipliers are identified for each type of problem. Examples are given at the end, which shows that this modification demonstrated the high efficiency and attained very good agreement in illustrated models and might be promptly reached out to other nonlinear differential and partial differential equations.