Browsing by Subject "Strongly nonlinear system"

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    A new perturbation solution for systems with strong quadratic and cubic nonlinearities
    (2010) Pakdemirli M.; Karahan M.M.F.
    The new perturbation algorithm combining the method of multiple scales (MS) and Lindstedt-Poincare techniques is applied to an equation with quadratic and cubic nonlinearities. Approximate analytical solutions are found using the classical MSmethod and the new method. Both solutions are contrasted with the direct numerical solutions of the original equation. For the case of strong nonlinearities, solutions of the new method are in good agreement with the numerical results, whereas the amplitude and frequency estimations of classical MS yield high errors. For strongly nonlinear systems, exact periods match well with the new technique while there are large discrepancies between the exact and classical MS periods. Copyright © 2009 John Wiley & Sons, Ltd.
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    Forced vibrations of strongly nonlinear systems with multiple scales lindstedt poincare method
    (Association for Scientific Research, 2011) Pakdemirli M.; Karahan M.M.F.; Boyaci H.
    Forced vibrations of duffing equation with damping is considered. Recently developed Multiple Scales Lindstedt-Poincare (MSLP) technique for free vibrations is applied for the first time to the forced vibration problem in search of approximate solutions. For the case of weak and strong nonlinearities, approximate solutions of the new method are contrasted with the usual Multiple Scales (MS) method and numerical simulations. For weakly nonlinear systems, frequency response curves of both perturbation methods and numerical solutions are in good agreement. For strongly nonlinear systems however, results of MS deviate much from the MSLP method and numerical simulations, the latter two being in good agreement. Keywords- Perturbation Methods, Lindstedt Poincare method, Multiple. © Association for Scientific Research.
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    Vibration analysis of a beam on a nonlinear elastic foundation
    (Techno-Press, 2017) Karahan M.M.F.; Pakdemirli M.
    Nonlinear vibrations of an Euler-Bernoulli beam resting on a nonlinear elastic foundation are discussed. In search of approximate analytical solutions, the classical multiple scales (MS) and the multiple scales Lindstedt Poincare (MSLP) methods are used. The case of primary resonance is investigated. Amplitude and phase modulation equations are obtained. Steady state solutions are considered. Frequency response curves obtained by both methods are contrasted with each other with respect to the effect of various physical parameters. For weakly nonlinear systems, MS and MSLP solutions are in good agreement. For strong hardening nonlinearities, MSLP solutions exhibit the usual jump phenomena whereas MS solutions are not reliable producing backward curves which are unphysical. Copyright © 2017 Techno-Press, Ltd.