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Shock and Vibration
Volume 19, Issue 3, Pages 323-332

Nonlinear Vibration of Oscillation Systems using Frequency-Amplitude Formulation

A. Fereidoon,1 M. Ghadimi,2 A. Barari,3 H.D. Kaliji,4 and G. Domairry2

1Department of Mechanical Engineering, Faculty of Engineering, Semnan University, Semnan, Iran
2Department of Mechanical Engineering, Babol University of Technology, Babol, Iran
3Department of Civil Engineering, Aalborg University, Sohngårdsholmsvej 57, 9000 Aalborg, Aalborg, Denmark
4Department of Mechanical Engineering, Islamic Azad University, Semnan Branch, Semnan, Iran

Received 9 October 2010; Revised 3 January 2011

Copyright © 2012 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper we study the periodic solutions of free vibration of mechanical systems with third and fifth-order nonlinearity for two examples using He's Frequency-Amplitude Formulation (HFAF).The effectiveness and convenience of the method is illustrated in these examples. It will be shown that the solutions obtained with current method have a fabulous conformity with those achieved from time marching solution. HFAF is easy with powerful concepts and the high accuracy, so it can be found widely applicable in vibrations, especially strong nonlinearity oscillatory problems.