Title: The analysis of free vibration of conservative oscillators with inertia and static type cubic non-linearities by variational-Padé technique

Authors: Mohammad Fesanghary; Zong Woo Geem

Addresses: Department of Mechanical Engineering, Louisiana State University, Baton Rouge, LA 70803, USA ' Department of Energy and Information Technology, Gachon University, Seongnam, 461-701, South Korea

Abstract: In this study, a new method based on the variational iteration method and the Padé approximation is introduced to obtain accurate analytical solutions for some special types of non-linear differential equations, arising in modelling the dynamic behaviour of oscillators with inertia together with cubic stiffness non-linearities. The comparison of the results of a new proposed variational Padé technique for analysing large-amplitude free vibrations of cantilever beams carrying a lumped mass and rotary inertia, with those of other conventional methods, ensures the excellent accuracy of the proposed method.

Keywords: variational iteration method; VIM; Padé approximation; nonlinear analysis; large amplitude vibration; free vibration; conservative oscillators; roatary inertia; cubic stiffness nonlinearities; nonlinear differential equations; modelling; oscillator dynamics; cantilever beams; lumped mass.

DOI: 10.1504/IJMMNO.2013.055200

International Journal of Mathematical Modelling and Numerical Optimisation, 2013 Vol.4 No.2, pp.103 - 113

Received: 28 Jun 2012
Accepted: 28 Jan 2013

Published online: 22 Jul 2013 *

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