c  Copyright, Darbose International Journal of Applied Mathematics and Computation Volume 2(3),pp 33–43, 2010 http://ijamc.psit.in Application of Hes variational approach method for periodic solution of strongly nonlinear oscillation problems A. Amani 1 , D. D. Ganji 2 , A. Ahmadi Jebelli 1 , M. Shahabi 1 , N. Safara Nosar 2 1 Department of Mechanical Engineering, Imam Hossein University, Tehran, Iran Email:amin amani81@yahoo.com 2 Department of Mechanical Engineering Babol University of Technology, Babol, Iran Abstract: Applications of He’s Variational Approach Method (VAM) to solve the nonlinear oscillations is discussed in this paper. We established approximate analytical formulas for the period periodic solution. In contrast with conven- tional methods, in VAM, only one iteration leads to high accuracy towards solutions. The attained results are logical for the whole solution domain with high preciseness. We find that VAM is excellently for the whole range of ini- tial amplitudes. VAM is in an excellent agreement of the periodical solutions with the Exact or other analytical solutions which has been demonstrated and discussed. Keywords: He’s Variational Approach; Nonlinear Oscillation; Mixed Parity Nonlinear; Ball-Bearing Oscillating; Weakly Nonlinear System. 1 Introduction Nonlinear analytical techniques for solving non-natural problems have been domi- nated by different methods. Investigate of nonlinear problems which are arisen in many areas of physics and also engineering is very important for scientists. Corresponding author: A. Amani