Browsing by Author "Öz H.R."

Now showing 1 - 15 of 15
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    Non-liner vibrations of a beam-mass system under different boundary conditions
    (Academic Press, 1997) Özkaya E.; Pakdemirli M.; Öz H.R.
    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. © 1997 Academic Press Limited.
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    Non-linear vibrations of a slightly curved beam resting on anon-linear elastic foundation
    (Academic Press, 1998) Öz H.R.; Pakdemirli M.; Özkaya 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. © 1998 Academic Press Limited.
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    Vibrations of an axially moving beam with time-dependent velocity
    (Academic Press, 1999) Öz H.R.; Pakdemirli M.
    The dynamic response of an axially accelerating, elastic, tensioned beam is investigated. The time-dependent velocity is assumed to vary harmonically about a constant mean velocity. These systems experience a coriolis acceleration component which renders such systems gyroscopic. The equation of motion is solved by using perturbation analysis. Principal parametric resonances and combination resonances are investigated in detail. Stability boundaries are determined analytically. It is found that instabilities occur when the frequency of velocity fluctuations is close to two times the natural frequency of the constant velocity system or when the frequency is close to the sum of any two natural frequencies. When the velocity variation frequency is close to zero or to the difference of two natural frequencies, however, no instabilities are detected up to the first order of perturbation. Numerical results are presented for different flexural stiffness values and for the first two modes. © 1999 Academic Press.
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    Transverse vibrations of tensioned pipes conveying fluid with time-dependent velocity
    (Academic Press Ltd, 2000) Öz H.R.; Boyaci H.
    In this study, the transverse vibrations of highly tensioned pipes with vanishing flexural stiffness and conveying fluid with time-dependent velocity are investigated. Two different cases, the pipes with fixed-fixed end and fixed-sliding end conditions are considered. The time-dependent velocity is assumed to be a harmonic function about a mean velocity. These systems experience a Coriolis acceleration component which renders such systems gyroscopic. The equation of motion is derived using Hamilton's principle and solved analytically by direct application of the method of multiple scales (a perturbation technique). The natural frequencies are found. Increasing the ratio of fluid mass to the total mass per unit length increases the natural frequencies. The principal parametric resonance cases are investigated in detail. Stability boundaries are determined analytically. It is found that instabilities occur when the frequency of velocity fluctuations is close to two times the natural frequency of the constant velocity system. When the velocity fluctuation frequency is close to zero, no instabilities are detected up to the first order of perturbation. Numerical results are presented for the first two modes.
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    Non-linear vibrations and stability of an axially moving beam with time-dependent velocity
    (Elsevier Science Ltd, 2001) Öz H.R.; Pakdemirli M.; Boyaci H.
    Non-linear vibrations of an axially moving beam are investigated. The non-linearity is introduced by including stretching effect of the beam. The beam is moving with a time-dependent velocity, namely a harmonically varying velocity about a constant mean velocity. Approximate solutions are sought using the method of multiple scales. Depending on the variation of velocity, three distinct cases arise: (i) frequency away from zero or two times the natural frequency, (ii) frequency close to zero, (iii) frequency close to two times the natural frequency. Amplitude-dependent non-linear frequencies are derived. For frequencies close to two times the natural frequency, stability and bifurcations of steady-state solutions are analyzed. For frequencies close to zero, it is shown that the amplitudes are bounded in time.
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    On the vibrations of an axially travelling beam on fixed supports with variable velocity
    (Academic Press, 2001) Öz H.R.
    [No abstract available]
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    Determination of natural frequencies and stability regions of axially moving beams using artificial neural networks method [3]
    (Academic Press, 2002) Özkaya E.; Öz H.R.
    [No abstract available]
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    Linear forced in-plane and out-of-plane vibrations of frames having a curved member
    (2004) Özyiǧit H.A.; Öz H.R.; Tekelioǧlu M.
    The forced, in-plane and out-of-plane vibrations of frames comprised of straight and curved members are investigated using Finite Element Methods. The straight and curved beams are assumed as Euler-Bernoulli type and they have circular cross-sections. The frame lies in a single plane. In the analysis, elongation, bending and rotary inertia effects are included. Four degrees of freedom for in-plane vibrations and three degrees of freedom for out-of-plane vibrations are assumed. The in-plane and out-of-plane point and transfer receptances are obtained in order to determine the sensitive and non-sensitive frequency interval of the frame system.
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    Natural frequencies of beam-mass systems in transverse motion for different end conditions
    (Association for Scientific Research, 2005) Öz H.R.; Özkaya E.
    In this study, an Euler-Bernoulli type beam carrying masses at different locations is considered. Natural frequencies for transverse vibrations are investigated for different end conditions. Frequency equations are obtained for two and three mass cases. Analytical and numerical results are compared with each other. © Association for Scientific Research.
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    Two-to-one internal resonances in a shallow curved beam resting on an elastic foundation
    (Springer Wien, 2006) Öz H.R.; 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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    Nonlinear transverse vibrations and 3:1 internal resonances of a beam with multiple supports
    (American Society of Mechanical Engineers(ASME), 2008) Özkaya E.; Baǧdatli S.M.; Öz H.R.
    In this study, nonlinear transverse vibrations of an Euler-Bernoulli beam with multiple supports are considered. The beam is supported with immovable ends. The immovable end conditions cause stretching of neutral axis and introduce cubic nonlinear terms to the equations of motion. Forcing and damping effects are included in the problem. The general arbitrary number of support case is considered at first, and then 3-, 4-, and 5-support cases are investigated The method of multiple scales is directly applied to the partial differential equations. Natural frequencies and mode shapes for the linear problem are found. The correction terms are obtained from the last order of expansion. Nonlinear frequencies are calculated and then amplitude and phase modulation figures are presented for different forcing and damping cases. The 3:1 internal resonances are investigated. External excitation frequency is applied to the first mode and responses are calculated for the first or second mode. Frequency-response and force-response curves are drawn. Copyright © 2008 by ASME.
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    Infinite mode analysis and truncation to resonant modes of axially accelerated beam vibrations
    (Academic Press, 2008) Pakdemirli M.; Öz H.R.
    The transverse vibrations of simply supported axially moving Euler-Bernoulli beams are investigated. The beam has a time-varying axial velocity with viscous damping. Traveling beam eigenfunctions with infinite number of modes are considered. Approximate analytical solutions are sought using the method of Multiple Scales, a perturbation technique. A detailed analysis of the resonances in which upto four modes of vibration involved are performed. Stability analysis is treated for each type of resonance. Approximate stability borders are given for the resonances involving only two modes. For higher number of modes involved in a resonance, sample numerical examples are presented for stabilities. © 2007 Elsevier Ltd. All rights reserved.
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    Non-linear transverse vibrations and 3:1 internal resonances of a tensioned beam on multiple supports
    (2011) Baǧdatli S.M.; Öz H.R.; Özkaya E.
    In this study, nonlinear transverse vibrations of a tensioned Euler-Bernoulli beam resting on multiple supports are investigated. The immovable end conditions due to simple supports cause stretching of neutral axis and introduce cubic nonlinearity to the equations of motion. Forcing and damping effects are included in the analysis. The general arbitrary number of support case is investigated and 3, 4, and 5 support cases analyzed in detail. A perturbation technique (the method of multiple scales) is applied to the equations of motion to obtain approximate analytical solutions. 3:1 internal resonance case is also considered. Natural frequencies and mode shapes for the linear problem are found for the tensioned beam. Nonlinear frequencies are calculated; amplitude and phase modulation figures are presented for different forcing and damping cases. Frequency-response and force-response curves are drawn. Different internal resonance cases between modes are investigated. © Association for Scientific Research.
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    Dynamics of axially accelerating beams with an intermediate support
    (American Society of Mechanical Engineers (ASME), 2011) Bagdatli S.M.; Özkaya E.; Öz H.R.
    The transverse vibrations of an axially accelerating EulerBernoulli beam resting on simple supports are investigated. The supports are at the ends, and there is a support in between. The axial velocity is a sinusoidal function of time varying about a constant mean speed. Since the supports are immovable, the beam neutral axis is stretched during the motion, and hence, nonlinear terms are introduced to the equations of motion. Approximate analytical solutions are obtained using the method of multiple scales. Natural frequencies are obtained for different locations of the support other than end supports. The effect of nonlinear terms on natural frequency is calculated for different parameters. Principal parametric resonance occurs when the velocity fluctuation frequency is equal to approximately twice of natural frequency. By performing stability analysis of solutions, approximate stable and unstable regions were identified. Effects of axial velocity and location of intermediate support on the stability regions have been investigated. Copyright © 2011 by ASME.
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    Dynamics of axially accelerating beams with multiple supports
    (Kluwer Academic Publishers, 2013) Bağdatli S.M.; Özkaya E.; Öz H.R.
    This study represents the transverse vibrations of an axially accelerating Euler-Bernoulli beam resting on multiple simple supports. This is one of the examples of a system experiencing Coriolis acceleration component that renders such systems gyroscopic. A small harmonic variation with a constant mean value for the axial velocity is assumed in the problem. The immovable supports introduce nonlinear terms to the equations of motion due to stretching of neutral axis. The method of multiple scales is directly applied to the equations of motion obtained for the general case. Natural frequency equations are presented for multiple support case. Principal parametric resonances and combination resonances are discussed. Solvability conditions are presented for different cases. Stability analysis is conducted for the solutions; approximate stable and unstable regions are identified. Some numerical examples are presented to show the effects of axial speed, number of supports, and their locations. © 2013 The Author(s).