Browsing by Publisher "ACADEMIC PRESS LTD"

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    Transverse vibrations of tensioned pipes conveying fluid with time-dependent velocity
    (ACADEMIC PRESS LTD) 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
    (ACADEMIC PRESS LTD) 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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    A comparison of different versions of the method of multiple scales for partial differential equations
    (ACADEMIC PRESS LTD) Boyaci, H; Pakdemirli, M
    Applications of the methods of multiple scales (a perturbation method) to partial differential systems arising in non-linear vibrations of continuous systems are considered. Two different versions of the method of multiple scales are applied to two general non-linear models. In one of the models, the small parameter (epsilon) multiplies an arbitrary non-linear cubic operator whereas in the other model, arbitrary quadratic and cubic non-linearities exist. The linear parts of both models are represented by arbitrary operators. General solutions are found by applying different versions of the method of multiple scales. Results of the first version (reconstitution method) and the second version (proposed by Rahman and Burton [8]) are compared for both models. From the comparisons of both methods, it is found that the second version yields better results. Applications of the general models to specific problems are also presented. A final recommendation is to use the second version of the method of multiple scales combined with the direct-perturbation method in finding steady state solutions of partial differential equations. (C) 1997 Academic Press Limited.
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    Non-linear vibrations of a beam-mass system with both ends clamped
    (ACADEMIC PRESS LTD) Özkaya, E; Pakdemirli, M
    A clamped-clamped beam-mass system is considered. The non-linear equations of motion including stretching due to immovable end conditions were derived previously [1] (Ozkaya et al. 1997 Journal of Sound and Vibration 199, 679-696). In addition to five different end conditions considered in reference [1], the case of clamped-clamped edge conditions is treated in this work. Exact solutions for the mode shapes and frequencies are given for the linear part of the problem. For the non-linear problem, approximate solutions using perturbations are searched, Alternatively, the natural frequencies and non-linear corrections are used in training a multi-layer, feed-forward, back propagation artificial neural network (ANN) algorithm. Using the algorithm, the numerical calculations are drastically reduced for obtaining the natural frequencies and non-linear corrections corresponding to different input parameters. (C) 1999 Academic Press.
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    Non-liner vibrations of a beam-mass system under different boundary conditions
    (ACADEMIC PRESS LTD) 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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    Vibrations of continuous systems with a general operator notation suitable for perturbative calculations
    (ACADEMIC PRESS LTD) Pakdemirli, M
    The operator notation previously developed to analyze vibrations of continuous systems has been further generalized to model a system with an arbitrary number of coupled differential equations. Linear parts of the equations are expressed with an arbitrary linear differential and/or integral operators, and non-linear parts are expressed with arbitrary quadratic and cubic operators. Equations of motion are solved in their general form using the method of multiple scales, a perturbation technique. The case of primary resonances of the external excitation and one-to-one internal resonances between the natural frequencies of the equations is considered. The algorithm developed is applied to a non-linear cable vibration problem having small sag-to-span ratios. (C) 2001 Academic Press.
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    Lie group theory and analytical solutions for the axially accelerating string problem
    (ACADEMIC PRESS LTD) Özkaya, E; Pakdemirli, M
    Transverse vibrations of a string moving with time-dependent velocity upsilon(t) have been investigated. Analytical solutions of the problem are found using the systematic approach of Lie group theory. Group classification with respect to the arbitrary velocity function has been performed using a newly developed technique of equivalence transformations. From the symmetries of the partial differential equation, the method for deriving exact solutions for the arbitrary velocity case is shown. Special cases of interest such as constant velocity, constant acceleration, harmonically varying velocity and exponentially decaying velocity are investigated in detail. Finally, for a simply supported strip, approximate solutions are presented for the exponentially decaying and harmonically varying cases. (C) 2000 Academic Press.
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    Stability analysis of an axially accelerating string
    (ACADEMIC PRESS LTD) Pakdemirli, M; Ulsoy, AG
    The dynamic response of an axially accelerating string is investigated. The time dependent velocity is assumed to vary harmonically about a constant mean velocity. Approximate analytical solutions are sought using two different approaches. In the first approach, the equations are discretized first and then the method of multiple scales is applied to the resulting equations. In the second approach, the method of multiple scales is applied directly to the partial differential system. 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 a band-saw and a threadline problem. (C) 1997 Academic Press Limited.
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