Higher order approximate periodic solutions for nonlinear oscillators with the Hamiltonian approach
Articles > Article ยท 2011
Authors: Ahmet YILDIRIM, Z. SAADATNIA, H. ASKARI, Y. KHAN, M. KALAMIYAZDI
Applied Mathematics Letters, Journal Indexed in SCI Expanded, International, WoS, 2011, vol 24, pp 2042-2051
DOI: 10.1016/j.aml.2011.05.040
Summary
In this work, the Hamiltonian approach is applied to obtain the natural frequency of the Duffing oscillator, the nonlinear oscillator with discontinuity and the quintic nonlinear oscillator. The Hamiltonian approach is then extended to the second and third orders to find more precise results. The accuracy of the results obtained is examined through time histories and error analyses for different values for the initial conditions. Excellent agreement of the approximate frequencies and the exact solution is demonstrated. It is shown that this method is powerful and accurate for solving nonlinear conservative oscillatory systems. (C) 2011 Elsevier Ltd. All rights reserved.