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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 620267, 6 pages
Optimal Variational Method for Truly Nonlinear Oscillators
1Faculty of Mechanical Engineering, “Politehnica” University of Timişoara, Bd. M. Viteazu, 1, 300222 Timişoara, Romania
2Center of Advanced Research in Engineering Sciences, Romanian Academy, Timişoara Branch, Bd. M. Viteazu, 24, 300223, Timişoara, Romania
Received 6 August 2012; Accepted 19 November 2012
Academic Editor: Kale Oyedeji
Copyright © 2013 Vasile Marinca and Nicolae Herişanu. 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.
- A. H. Nayfeh and D. T. Mook, Nonlinear Oscillations, John Wiley and Sons, New York, NY, USA, 1979.
- P. Hagedorn, Nonlinear Oscillations, vol. 10, Clarendon Press, Oxford, UK, 1988.
- R. E. Mickens, Oscillations in Planar Dynamical Systems, vol. 37, World Scientific, Singapore, 1996.
- J.-H. He, “Modified Lindstedt-Poincare methods for some strongly nonlinear oscillators. Part.I. expansion of a constant,” International Journal of Non-Linear Mechanics, vol. 37, no. 2, pp. 309–314, 2002.
- A. Beléndez, C. Pascual, C. Neipp, T. Beléndez, and A. Hernández, “An equivalent linearization method for conservative nonlinear oscillators,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 9, no. 1, pp. 9–17, 2008.
- J. I. Ramos, “Linearized Galerkin and artificial parameter techniques for the determination of periodic solutions of nonlinear oscillators,” Applied Mathematics and Computation, vol. 196, no. 2, pp. 483–493, 2008.
- G. Adomian, “A review of the decomposition method in applied mathematics,” Journal of Mathematical Analysis and Applications, vol. 135, no. 2, pp. 501–544, 1988.
- V. Marinca and N. Herişanu, “Determination of periodic solutions for the motion of a particle on a rotating parabola by means of the optimal homotopy asymptotic method,” Journal of Sound and Vibration, vol. 329, no. 9, pp. 1450–1459, 2010.
- V. Marinca and N. Herişanu, Nonlinear Dynamical Systems in Engineering. Some Approximate Approaches, Springer, Berlin, Germany, 2011.
- N. Herişanu and V. Marinca, “A modified variational iteration method for strongly nonlinear problems,” Nonlinear Science Letters A, vol. 1, pp. 183–192, 2010.
- J. H. He, “Preliminary report on the energy balance for nonlinear oscillations,” Mechanics Research Communications, vol. 29, pp. 107–111, 2003.
- V. Obădeanu and V. Marinca, The Inverse Problem in Analytic Mechanics, University of Timişoara, Timişoara, Romania, 1992.
- R. E. Mickens and K. Oyedeji, “Construction of approximate analytical solutions to a new class of nonlinear oscillator equation,” Journal of Sound and Vibration, vol. 162, no. 4, pp. 579–582, 1985.
- R. E. Mickens, “A generalized iteration procedure for calculating approximations to periodic solutions of ‘truly nonlinear oscillators’,” Journal of Sound and Vibration, vol. 287, no. 4-5, pp. 1045–1051, 2005.
- R. E. Mickens, “Iteration method solutions for conservative and limit-cycle X1/3 force oscillators,” Journal of Sound and Vibration, vol. 292, no. 3–5, pp. 964–968, 2006.