Nonlinear vibrations of axially moving multi-supported strings having non-ideal support conditions

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...

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Bibliographic Details
Published in:Nonlinear dynamics 2013-08, Vol.73 (3), p.1223-1244
Main Authors: Yurddas, A, Ozkaya, E, Boyaci, H
Format: Article
Language:English
Subjects:
Automotive Engineering
Boundaries
Boundary conditions
Classical Mechanics
Control
Dependence
Dynamical Systems
Engineering
Equations of motion
Frequency stability
Frequency variation
Mathematical analysis
Mechanical Engineering
Multiscale analysis
Nonlinear equations
Nonlinearity
Original Paper
Perturbation methods
Stability
Stability analysis
Strings
Vibration
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Summary: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.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-012-0650-5