An analytical approximate technique to investigate a finite extensibility nonlinear oscillatorFootnote

Peer review under responsibility of University of Bahrain.

References

• M.AkbarzadeY.KhanDynamic model of large amplitude non-linear oscillations arising in the structural engineering: analytical solutionsMath. Comput. Modell.552012480489
   Google Scholar
• M.S.AlamM.E.HaqueM.B.HossianA new analytical technique to find periodic solutions of nonlinear systemsInt. J. Nonlinear Mech.42200710351045
   Google Scholar
• P.AmoreA.ArandaImproved Lindstedt-Poincare method for the solution of nonlinear problemsJ. Sound Vib.2833–5200511151136
   Web of Science ®Google Scholar
• A.BelendezC.PascualS.GallegoM.OrtunoC.NeippApplication of a modified He’s homotopy perturbation method to obtain higher-order approximation of an x1/3 force nonlinear oscillatorPhys. Lett. A3712007421426
   Google Scholar
• A.BeléndezE.ArribasJ.FrancésI.PascualComments on A finite extensibility nonlinear oscillatorAppl. Math. Comput.218201261686175
   Google Scholar
• N.N.BogoliubovYu.A.MitropolskiiAsymptotic Methods in the Theory of Nonlinear Oscillations1961Gordan and BreachNew York
   Google Scholar
• Y.K.CheungS.H.MookS.L.LauA modified Lindstedt-Poincare method for certain strongly nonlinear oscillatorsInt. J. Nonlinear Mech.261991367378
   Web of Science ®Google Scholar
• R.EllahiM.HassanA.ZeeshanShape effects of nanosize particles in Cu-H2O nanofluid on entropy generationInt. J. Heat Mass Transfer812015449456
   Web of Science ®Google Scholar
• R.EllahiM.HassanA.ZeeshanStudy of natural convection MHD nanofluid by means of single and multi walled carbon nanotubes suspended in a salt water solutions NanotechnologyIEEE Trans.1442015726734
   Google Scholar
• M.FebboA finite extensibility nonlinear oscillatorAppl. Math. Comput.217201164646475
   Google Scholar
• M.FebboA.MilchevV.RostiashviliD.DimitrovT.A.VilgisDynamics of a stretched nonlinear polymer chainChem. Phys.1292008154908115490813
   Google Scholar
• J.W.HatfieldS.R.QuakeDynamic properties of an extended polymer in solutionPhys. Rev. Lett.82199935483551
   Web of Science ®Google Scholar
• J.H.HeModified Lindstedt-Poincare methods for some strongly nonlinear oscillations-I: expansion of a constantInt. J. Nonlinear Mech.372002309314
   Web of Science ®Google Scholar
• M.A.HosenM.S.H.ChowdhuryA new reliable analytical solution for strongly nonlinear oscillator with cubic and harmonic restoring forceResults Phys.52015111114
   Google Scholar
• M.A.HosenM.S.RahmanM.S.AlamM.R.AminAn analytical technique for solving a class of strongly nonlinear conservative systemsAppl. Math. Comput.218201254745486
   Google Scholar
• M.M.M.JoubariH.J.JouybariM.H.PashaeiSolution of strongly nonlinear oscillator problem arising in Plasma Physics with Newton Harmonic Balance MethodJ. Appl. Comput. Mech.1220155966
   Google Scholar
• Y.KhanM.AkbarzadeDynamic analysis of non-linear oscillator equation arising in double-sided driven clamped microbeam-based electromechanical resonatorZ. Naturforsch., A672012435440
   Google Scholar
• Y.KhanA.MirzabeigyImproved accuracy of He’s energy balance method for analysis of conservative nonlinear oscillatorNeural Comput. Appl.252014889895
   Google Scholar
• Y.KhanM.MadaniA.YildirimM.A.AbdouN.FarazA new approach to van der pol's oscillator problemZ. Naturforsch., A662011620624
   Google Scholar
• Y.KhanM.AkbarzadeA.KargarCoupling of homotopy and variational approach for a conservative oscillator with strong odd-nonlinearityScientia Iranica1932012417422
   Google Scholar
• Y.KhanH.V.LealN.FarazAn efficient new iterative method for oscillator differential equationScientia Iranica196201214731477
   Google Scholar
• Y.KhanM.K.YazdiH.AskariZ.SaadatniaDynamic analysis of generalized conservative nonlinear oscillators via frequency amplitude formulationArabian J. Sci. Eng.3812013175179
   Google Scholar
• J.KoplikJ.R.BanavarExtensional rupture of model non-Newtonian fluid filamentsPhys. Rev. E6720031150211150212
   Google Scholar
• N.N.KrylovN.N.BogoliubovIntroduction to Nonlinear Mechanics1947Princeton University PressNew Jersey
   Google Scholar
• C.W.LimS.K.LaiB.S.WuAccurate higher-order analytical approximate solutions to large-amplitude oscillating systems with general non-rational restoring forceJ. Nonlinear Dyn.422005267281
   Google Scholar
• J.B.MarionClassical Dynamics of Particles and System1970Harcourt Brace JovanovichSan Diego, CA
   Google Scholar
• R.E.MickensComments on the method of harmonic balanceJ. Sound Vib.941984456460
   Web of Science ®Google Scholar
• R.E.MickensOscillation in Planar Dynamic Systems1996World ScientificSingapore
   Google Scholar
• M.NawazA.ZeeshanR.EllahiS.AbbasbandyS.RashidiJoules and Newtonian heating effects on stagnation point flow over a stretching surface by means of genetic algorithm and Nelder-Mead methodInt. J. Numer. Meth. Heat Fluid Flow2532015665684
   Google Scholar
• A.H.NayfehD.T.MookNonlinear Oscillations1979John Wiley & SonsNew York
   Google Scholar
• M.M.RashidiF.MohammadiS.AbbasbandyM.S.AlhuthaliEntropy generation analysis for stagnation point flow in a porous medium over a permeable stretching surfaceJ. Appl. Fluid Mech.842015753765
   Google Scholar
• M.A.RazzakA simple harmonic balance method for solving strongly nonlinear oscillatorsJ. Assoc. Arab Univ. Basic Appl. Sci.2120166876
   Google Scholar
• R.S.SahaA.PatraHaar wavelet operational methods for the numerical solutions of fractional order nonlinear oscillatory van der pol systemAppl. Math. Comput.2202013659667
   Google Scholar
• B.S.WuW.P.SunC.W.LimAn analytical approximate technique for a class of strongly nonlinear oscillatorsInt. J. Nonlinear Mech.412006766774
   Web of Science ®Google Scholar
• D.XuJ.CuiS.LiaoA.AlsaediA HAM-based analytic approach for physical models with an infinite number of singularitiesNumer. Algorithms69120155974
   Google Scholar
• M.K.YazdiY.KhanM.MadaniH.AskariZ.SaadatniaA.YildirimAnalytical solutions for autonomous conservative nonlinear oscillatorInt. J. Nonlinear Sci. Numer. Simulat.11112010979984
   Web of Science ®Google Scholar
• A.YildirimZ.SaadatniaH.AskariY.KhanM.K.YazdiHigher order approximate periodic solutions for nonlinear oscillators with the Hamiltonian approachAppl. Math. Lett.2412201120422051
   Google Scholar
• A.YildirimH.AskariZ.SaadatniaM.K.YazdiY.KhanAnalysis of nonlinear oscillations of a punctual charge in the electric field of a charged ring via a Hamiltonian approach and the energy balance methodComput. Math. Appl.622011486490
   Web of Science ®Google Scholar
• A.YildirimH.AskariM.K.YazdiY.KhanA relationship between three analytical approaches for the nonlinear problemsAppl. Math. Lett.25201217291733
   Google Scholar
• A.ZeeshanM.BaigR.EllahiT.HayatFlow of viscous nanofluid between the concentric cylindersJ. Comput. Theor. Nanosci.1132014646654
   Google Scholar
• Zhong, X., Liao, S., 2016. Analytic Solutions of Von Karman Plate under Arbitrary Uniform Pressure (II): Equations in Integral Form. arXiv preprint arXiv:1604.06711.
   Google Scholar