On the approximate analytical solution to non-linear oscillation systems

Article type: Research Article

Authors: Bayat, Mahmoud | Pakar, Iman

Affiliations: Department of Civil Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran

Note: [] Corresponding author: Mahmoud Bayat, Department of Civil Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran. E-mail: mbayat14@yahoo.com

Abstract: This study describes an analytical method to study two well-known systems of nonlinear oscillators. One of these systems deals with the strongly nonlinear vibrations of an elastically restrained beam with a lumped mass. The other is a Duffing equation with constant coefficients. A new implementation of the Variational Approach (VA) is presented to obtain highly accurate analytical solutions to free vibration of conservative oscillators with inertia and static type cubic nonlinearities. In the end, numerical comparisons are conducted between the results obtained by the Variational Approach and numerical solution using Runge-Kutta's [RK] algorithm to illustrate the effectiveness and convenience of the proposed methods.

Keywords: Variational Approach (VA), nonlinear vibrations, analytical methods, Runge-Kutta's [RK] algorithm

DOI: 10.3233/SAV-2012-0726

Journal: Shock and Vibration, vol. 20, no. 1, pp. 43-52, 2013