Browsing by Subject "Forced vibration"

Now showing 1 - 4 of 4
  • No Thumbnail Available
    Item
    A general solution procedure for the forced vibrations of a continuous system with cubic nonlinearities: Primary resonance case
    (2009) Burak Özhan B.; Pakdemirli M.
    Nonlinear vibrations of a general model of continuous system is considered. The model consists of arbitrary linear and cubic operators. The equation of motion is solved by the method of multiple scales (a perturbation method). The primary resonances of external excitation is analysed. The amplitude and phase modulation equations are presented. Approximate analytical solution is derived. Steady-state solutions and their stability are discussed. Finally, the solution algorithm is applied to two different engineering problems. One of the application is the transverse vibration of an axially moving Euler-Bernoulli beam and the other is a viscoelastic beam. © 2009.
  • No Thumbnail Available
    Item
    A general solution procedure for the forced vibrations of a system with cubic nonlinearities: Three-to-one internal resonances with external excitation
    (2010) Burak Özhan B.; Pakdemirli M.
    A general vibrational model of a continuous system with arbitrary linear and cubic operators is considered. Approximate analytical solutions are found using the method of multiple scales. The primary resonances of the external excitation and three-to-one internal resonances between two arbitrary natural frequencies are treated. The amplitude and phase modulation equations are derived. The steady-state solutions and their stability are discussed. The solution algorithm is applied to two specific problems: (1) axially moving Euler-Bernoulli beam, and (2) axially moving viscoelastic beam. © 2010 Elsevier Ltd. All rights reserved.
  • No Thumbnail Available
    Item
    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.
  • No Thumbnail Available
    Item
    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.