Browsing by Subject "Axially moving strings"

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    Nonlinear vibrations of axially moving multi-supported strings having non-ideal support conditions
    (Kluwer Academic Publishers, 2013) Yurddaş A.; Özkaya E.; Boyacı H.
    In this study, nonlinear vibrations of an axially moving multi-supported string have been investigated. The main difference of this study from the others is in that there are non-ideal supports allowing minimal deflections between ideal supports at both ends of the string. Nonlinear equations of the motion and boundary conditions have been obtained using Hamilton's Principle. Dependence of the equations of motion and boundary conditions on geometry and material of the string have been eliminated by non-dimensionalizing. Method of multiple scales, a perturbation technique, has been employed for solving the equations of motion. Axial velocity has been assumed a harmonically varying function about a constant value. Axially moving string has been investigated in three regions. Vibrations have been examined for three different cases of the velocity variation frequency. Stability has been analyzed and stability boundaries have been established for the principal parametric resonance case. Effects of the non-ideal support conditions on stability boundaries and vibration amplitudes have been investigated. © 2012 Springer Science+Business Media Dordrecht.
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    Nonlinear vibrations and stability analysis of axially moving strings having nonideal mid-support conditions
    (2014) Yurddaş 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 Ω. 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. © The Author(s) 2012 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav.
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    Nonlinear vibrations of spring-supported axially moving string
    (Kluwer Academic Publishers, 2015) Kesimli A.; Özkaya E.; Bağdatli S.M.
    In this study, multi-supported axially moving string is discussed. Supports located at the ends of the string are simple supports. A support located in the middle section owns the features of a spring. String speed is assumed to vary harmonically around an average rate. Hamilton’s principle has been used to figure out the nonlinear equations of motion and boundary conditions. These equations and boundary conditions are dimensionless. Considering the nonlinear effects caused by the string extensions, nonlinear equations of motion are obtained. By using multi-timescaled method, which is one of the perturbation methods, approximate solutions have been found. The first term in the perturbation series causes the linear problem. With the solution of the linear problem, exact natural frequencies have been calculated for different locations of the supports on the middle, various spring coefficients and, with the spring support in the middle of the different location, different spring coefficient and axial speed values. Nonlinear terms on second order add correction terms to the linear problem. Effect of nonlinear terms on the natural frequency has been calculated for various parameters. The cases when the changing frequency of speed is equal to zero, close to zero and close to two times of the natural frequency have been analyzed separately. For each case, the stable and unstable areas in the solutions have been identified by stability analysis. © 2015, Springer Science+Business Media Dordrecht.