Browsing by Author "Öz, HR"

Now showing 1 - 11 of 11
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    Infinite mode analysis and truncation to resonant modes of axially accelerated beam vibrations
    Pakdemirli, M; Öz, HR
    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. (c) 2007 Elsevier Ltd. All rights reserved.
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    Nonlinear transverse vibrations and 3:1 internal resonances of a beam with multiple supports
    Özkaya, E; Bagdatli, SM; Öz, HR
    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.
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    Two-to-one internal resonances in a shallow curved beam resting on an elastic foundation
    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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    Dynamics of axially accelerating beams with multiple supports
    Bagdatli, SM; Özkaya, E; Öz, HR
    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.
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    Non-linear vibrations and stability analysis of tensioned pipes conveying fluid with variable velocity
    Öz, HR
    In this study, the non-linear transverse vibrations of highly tensioned pipes with vanishing flexural stiffness and conveying fluid with variable velocity art: investigated. The pipe is on fixed supports and the immovable end conditions result in the extension of the pipe during vibration and hence introduce further non-linear terms to the equation of motion. The 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 solved analytically bq. direct application of the method of multiple scales (a perturbation technique). Principal parametric resonance cases are investigated in detail. Non-linear frequencies are derived depending on amplitude. 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. (C) 2001 Elsevier Science Ltd. All rights reserved.
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    Non-linear vibrations and stability of an axially moving beam with time-dependent velocity
    Öz, HR; 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. (C) 2000 Elsevier Science Ltd. All rights reserved.
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    Transverse vibrations of tensioned pipes conveying fluid with time-dependent velocity
    Öz, HR; 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. (C) 2000 Academic Press.
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    Vibrations of an axially moving beam with time-dependent velocity
    Öz, HR; 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. (C) 1999 Academic Press.
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    Dynamics of Axially Accelerating Beams With an Intermediate Support
    Bagdatli, SM; Özkaya, E; Öz, HR
    The transverse vibrations of an axially accelerating Euler-Bernoulli 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. [DOI: 10.1115/1.4003205]