An Application of the Optimal Homotopy Asymptotic Method to Generalized Van der Pol Oscillator

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Abstract:

In this paper we illustrate the application of an alternative of the Optimal Homotopy Asymptotic Method (OHAM) to nonlinear generalized van der Pol oscillator. The obtained results proved a very fast convergence and validate this approach, which is found to be reliable and easy to use. Two numerical examples are developed in order to emphasize the accuracy and efficiency of the proposed approach.

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33-37

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October 2015

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© 2015 Trans Tech Publications Ltd. All Rights Reserved

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[1] A.H. Nayfeh, D.T. Mook, Nonlinear Oscillations, Wiley, New York, (1979).

Google Scholar

[2] J. Awrejcewicz, V.A. Krysko, Introduction to Asymptotic Methods, Chapman and Hall/CRC Press, (2006).

Google Scholar

[3] S. Ghosh, D. Roy, An adaptation of Adomian decomposition for numeric-analytic integration of strongly nonlinear and chaotic oscillators, Comp. Meth. Appl. Mech. Eng. 196 (2007) 1133-1153.

DOI: 10.1016/j.cma.2006.08.010

Google Scholar

[4] Y.M. Chen, J.K. Liu, Uniformly valid solution of limit cycle of the Duffing-van der Pol equation, Mech. Res. Commun. 36 (2009) 845-850.

DOI: 10.1016/j.mechrescom.2009.06.001

Google Scholar

[5] S. Momani, G.H. Erjaee, M.H. Alnasr, The modified homotopy perturbation method for solving strongly nonlinear oscillators, Comp. Math. Appl. 58 (2009) 2209-2220.

DOI: 10.1016/j.camwa.2009.03.082

Google Scholar

[6] V. Marinca, N. Herisanu, Periodic solutions of Duffing equation with strong non-linearity, Chaos, Soliton, Fractals 37 (2008) 144-149.

DOI: 10.1016/j.chaos.2006.08.033

Google Scholar

[7] N. Herişanu, V. Marinca, Optimal homotopy perturbation method for a non-conservative dynamical system of a rotating electrical machine, Zeitschrift fur Naturforsch. A 67 (2012) 509-516.

DOI: 10.5560/zna.2012-0047

Google Scholar

[8] L. Cveticanin, On the van der Pol oscillator: an overview, Appl. Mech. Mat. 430 (2013) 3-13.

Google Scholar

[9] I. Kovacic, R.E. Mickens, A generalized van der Pol type oscillator: Investigation of the properties of its limit cycle, Math. Comput. Model. 55 (2012) 645-653.

DOI: 10.1016/j.mcm.2011.08.038

Google Scholar

[10] K. Oyedeji, An analysis of a nonlinear elastic force van der Pol oscillator equation, J. Sound. Vibr. 281 (2005) 417-422.

DOI: 10.1016/j.jsv.2004.03.040

Google Scholar

[11] N. Herisanu, V. Marinca, An iteration procedure with application to van der Pol oscillator, Int. J. Nonlinear Sci. Num. Simul. 10 (2009) 353-361.

Google Scholar

[12] J. Warminski, Regular and chaotic vibrations of van der Pol and Rayleigh oscillators driven by parametric excitation, Procedia IUTAM. 5 (2012) 78-87.

DOI: 10.1016/j.piutam.2012.06.011

Google Scholar

[13] S. Natsiavas, Dynamics of piecewise linear oscillators with van der Pol type damping, Int. J. Non-Linear Mech. 26 (1991) 349-366.

DOI: 10.1016/0020-7462(91)90065-2

Google Scholar

[14] C.W. Lim, S.K. Lai, Accurate higher-order analytical approximate solutions to nonconservative nonlinear oscillators and application to van der Pol damped oscillators, Int. J. Mech. Sci. 48 (2006) 483-492.

DOI: 10.1016/j.ijmecsci.2005.12.009

Google Scholar

[15] V. Marinca, N. Herisanu, An optimal asymptotic approach to nonlinear MHD Jeffery-Hamel flow, Math. Probl. Eng., Art. No. 169056, (2011).

Google Scholar

[16] V. Marinca, N. Herisanu, The optimal homotopy asymptotic method. Engineering applications, Springer, (2015).

DOI: 10.1007/978-3-319-15374-2_2

Google Scholar