Browsing by Subject "CONTINUOUS SYSTEMS"

Now showing 1 - 4 of 4
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    Nonlinear transverse vibrations of a slightly curved beam carrying a concentrated mass
    (SPRINGER HEIDELBERG) Özkaya, E; Sarigül, M; Boyaci, H
    In this study, a slightly curved Euler Bernoulli beam carrying a concentrated mass was handled. The beam was resting on an elastic foundation and simply supported at both ends. Effects of the concentrated mass on nonlinear vibrations were investigated. Sinusoidal and parabolic type functions were used as curvature functions. Equations of motion have cubic nonlinearities because of elongations during vibrations. Damping and harmonic excitation terms were added to the equations of motion. Method of multiple scales, a perturbation technique, was used for solving integro-differential equation analytically. Natural frequencies were calculated exactly for different mass ratios, mass locations, curvature functions, and linear elastic foundation coefficients. Amplitude-phase modulation equations were found by considering primary resonance case. Effects of nonlinear terms on natural frequencies were calculated. Frequency-amplitude and frequency-response graphs were plotted. Finally effects of concentrated mass and chosen curvature function on nonlinear vibrations were investigated.
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    Two-to-one internal resonances in a shallow curved beam resting on an elastic foundation
    (SPRINGER WIEN) Öz, HR; Pakdemirli, M
    Vibrations of shallow curved beams are investigated. The rise function of the beam is assumed to be small. Sinusoidal and parabolic curvature functions are examined. The immovable end conditions result in mid-plane stretching of the beam which leads to nonlinearities. The beam is resting on an elastic foundation. The method of multiple scales, a perturbation technique, is used in search of approximate solutions of the problem. Two-to-one internal resonances between any two modes of vibration are studied. Amplitude and phase modulation equations are obtained. Steady state solutions and stability are discussed, and a bifurcation analysis of the amplitude and phase modulation equations are given. Conditions for internal resonance to occur are discussed, and it is found that internal resonance is possible for the case of parabolic curvature but not for that of sinusoidal curvature.
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    Vibration analysis of a beam on a nonlinear elastic foundation
    (TECHNO-PRESS) Karahan, MMF; 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.
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    Infinite mode analysis of a general model with external harmonic excitation
    (ELSEVIER SCIENCE INC) Sinir, BG
    This study proposes a general solution procedure for infinite mode analysis. The equation of motion is written in a general form using spatial differential operators, which are suitable for perturbation techniques. The multiple time scales method is applied directly to solve the proposed equation of motion. General investigations of some resonance cases are provided, such as parametric, sum type, difference type, and a combination of sum and difference type resonances. The proposed general solution procedure is applied to one- and two-dimensional problems. The results demonstrate that this general solution procedure obtains good solutions in the dynamic analysis of beams, plates, and other structures. (C) 2014 Elsevier Inc. All rights reserved.