Application of the Hamiltonian approach to nonlinear oscillators with rational and irrational elastic terms


YILDIRIM A. , SAADATNIA Z., ASKARI H.

MATHEMATICAL AND COMPUTER MODELLING, vol.54, pp.697-703, 2011 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 54
  • Publication Date: 2011
  • Doi Number: 10.1016/j.mcm.2011.03.012
  • Title of Journal : MATHEMATICAL AND COMPUTER MODELLING
  • Page Numbers: pp.697-703

Abstract

In this paper, Hamiltonian Approach (HA) is applied to obtain the analytical approximate solution of the nonlinear oscillators with Rational and Irrational Elastic Terms. Periodic solutions are analytically verified and consequently the relationship between the natural frequency and the initial amplitude is obtained in an analytical form. A comparison of the period of oscillation and obtained solutions with the exact results illustrates that the Hamiltonian approach is very effective and quite accurate for nonlinear equations. (C) 2011 Elsevier Ltd. All rights reserved.