Browsing by Subject "FORCED VIBRATIONS"

Now showing 1 - 6 of 6
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    Linear vibrations of continuum with fractional derivatives
    (SPRINGER) Demir, DD; Bildik, N; Sinir, BG
    In this paper, linear vibrations of axially moving systems which are modelled by a fractional derivative are considered. The approximate analytical solution is obtained by applying the method of multiple scales. Including stability analysis, the effects of variation in different parameters belonging to the application problems on the system are calculated numerically and depicted by graphs. It is determined that the external excitation force acting on the system has an effect on the stiffness of the system. Moreover, the general algorithm developed can be applied to many problems for linear vibrations of continuum.
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    Nonlinear vibrations and stability analysis of axially moving strings having nonideal mid-support conditions
    (SAGE PUBLICATIONS LTD) Yurddas, A; Özkaya, E; Boyaci, H
    In this study, nonlinear vibrations of an axially moving string are investigated. The main difference of this study from other studies is that there is a nonideal support between the opposite sides, which allows small displacements. Nonlinear equations of motion and boundary conditions are derived using Hamilton's principle. Equations of motion and boundary conditions are converted to nondimensional form. Thus, the equations become independent from geometry and material properties. The method of multiple scales, a perturbation technique, is used. A harmonically varying velocity function is chosen for modeling the axial movement. String as a continuous medium is investigated in two regions. Vibrations are investigated for three different cases of the excitation frequency . Stability analysis is carried out for these three cases, and stability boundaries are determined for the principle parametric resonance case. Thus, differences between ideal and nonideal boundary conditions are investigated.
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    Principal parametric resonances of a general continuous system with cubic nonlinearities
    (ELSEVIER SCIENCE INC) Özhan, BB; Pakdemirli, M
    A generalized vibrational model of cubic nonlinear continuous system with arbitrary parametric excitation is considered. The method of multiple scales (a perturbation method) is used to find an approximate analytical solution. The primary parametric resonance of the parametric excitation is considered. The amplitude and phase modulation equations are derived. Steady state solutions and their stability are discussed. The solution algorithm is applied to the problem of nonlinear vibrations of viscoelastic pipes conveying fluids. Natural frequencies of viscoelastic pipes are found. Frequency response curves and bifurcation points are drawn. Stable and unstable regions of trivial and nontrivial solutions are obtained. (C) 2012 Elsevier Inc. All rights reserved.
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    Size-dependent vibrations of a micro beam conveying fluid and resting on an elastic foundation
    (SAGE PUBLICATIONS LTD) Kural, S; Özkaya, E
    In this study, fluid conveying continuous media was considered as micro beam. Unlike the classical beam theory, the effects of shear stress on micro-structure's dynamic behavior not negligible. Therefore, modified couple stress theory (MCST) were used to see the effects of being micro-sized. By using Hamilton's principle, the nonlinear equations of motion for the fluid conveying micro beam were obtained. Micro beam was considered as resting on an elastic foundation. The obtained equations of motion were became independence from material and geometric structure by nondimensionalization. Approximate solutions of the system were achieved with using the multiple time scales method (a perturbation method). The effects of micro-structure, spring constant, the occupancy rate of micro beam, the fluid velocity on natural frequency and solutions were researched. MCST compared with classical beam theory and showed that beam models that based on classical beam theory are not capable of describing the size effects. Comparisons of classical beam theory and MCST were showed in graphics and these graphics also proved that obtained mathematical model suitable for describe the behavior of normal sized beams.
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    Effect of Viscoelasticity on the Natural Frequencies of Axially Moving Continua
    (HINDAWI PUBLISHING CORPORATION) Özhan, BB; Pakdemirli, M
    Linear models of axially moving viscoelastic beams and viscoelastic pipes conveying fluid are considered. The natural frequencies of the models are calculated. For both models, viscoelasticity terms are assumed to be of order one. Natural frequencies corresponding to various beam and pipe parameters are presented. Effects of viscoelasticity on the natural frequencies are discussed.
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    Infinite mode analysis of a general model with external harmonic excitation
    (ELSEVIER SCIENCE INC) Sinir, BG
    This study proposes a general solution procedure for infinite mode analysis. The equation of motion is written in a general form using spatial differential operators, which are suitable for perturbation techniques. The multiple time scales method is applied directly to solve the proposed equation of motion. General investigations of some resonance cases are provided, such as parametric, sum type, difference type, and a combination of sum and difference type resonances. The proposed general solution procedure is applied to one- and two-dimensional problems. The results demonstrate that this general solution procedure obtains good solutions in the dynamic analysis of beams, plates, and other structures. (C) 2014 Elsevier Inc. All rights reserved.