Araştırma Çıktıları | Scopus

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Browsing by Publisher "Academic Press Ltd"

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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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    Lie group theory and analytical solutions for the axially accelerating string problem
    (Academic Press Ltd, 2000) Özkaya E.; Pakdemirli M.
    Transverse vibrations of a string moving with time-dependent velocity v(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.
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    Vibrations of an axially accelerating beam with small flexural stiffness
    (Academic Press Ltd, 2000) Özkaya E.; Pakdemirli M.
    Transverse vibrations of an axially moving beam are considered. The axial velocity is harmonically varying about a mean velocity. The equation of motion is expressed in terms of dimensionless quantities. The beam effects are assumed to be small. Since, in this case, the fourth order spatial derivative multiplies a small parameter, the mathematical model becomes a boundary layer type of problem. Approximate solutions are searched using the method of multiple scales and the method of matched asymptotic expansions. Results of both methods are contrasted with the outer solution.