Browsing by Author "Oz, HR"

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    Non-liner vibrations of a beam-mass system under different boundary conditions
    Ozkaya, E; Pakdemirli, M; Oz, HR
    An Euler-Bernoulli beam and a concentrated mass on this beam are considered as a beam-mass system. The beam is supported by immovable end conditions, thus leading to stretching during the vibrations. This stretching produces cubic non-linearities in the equations. Forcing and damping terms are added into the equations. The dimensionless equations are solved for five different set of boundary conditions. Approximate solutions of the equations are obtained by using the method of multiple scales, a perturbation technique. The first terms of the perturbation series lead to the linear problem. Natural frequencies and mode shapes for the linear problem are calculated exactly for different end conditions. Second order non-linear terms of the perturbation series appear as corrections to the linear problem. Amplitude and phase modulation equations are obtained. Non-linear free and forced vibrations are investigated in detail. The effects of the position and magnitude of the mass, as well as effects of different end conditions on the vibrations, are determined. (C) 1997 Academic Press Limited.
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    Non-linear vibrations of a slightly curved beam resting on a non-linear elastic foundation
    Oz, HR; Pakdemirli, M; Ozkaya, E; Yilmaz, M
    In this study, non-linear vibrations of slightly curved beams are investigated. The curvature is taken as an arbitrary function of the spatial variable. The initial displacement is not due to buckling of the beam, but is due to the geometry of the beam itself. The ends of the curved beam are on immovable simple supports and the beam is resting on a non-linear elastic foundation. The immovable end supports result in the extension of the beam during the vibration and hence introduces further non-linear terms to the equations of motion. The integro-differential equations of motion are solved analytically by means of direct application of the method of multiple scales (a perturbation method). The amplitude and phase modulation equations are derived for the case of primary resonances. Both free and forced vibrations with damping are investigated. Effect of non-linear elastic foundation as well as the effect of curvature on the vibrations of the beam are examined. It is found that the effect of curvature is of softening type. For sufficiently high values of the coefficients, the elastic foundation may suppress the softening behaviour resulting in a hardening behaviour of the non-linearity. (C) 1998 Academic Press Limited.
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