On the transversal vibrations of an axially moving continuum with a time-varying velocity: Transient from string to beam behavior

2009 ◽  
Vol 325 (4-5) ◽  
pp. 959-973 ◽  
Author(s):  
S.V. Ponomareva ◽  
W.T. van Horssen
Keyword(s):  
Time Varying ◽  
Axially Moving ◽  
Transversal Vibrations

On the Transversal Vibrations of an Axially Moving Continuum With a Time-Varying Velocity: Transient From String to Beam Behavior

2007 ◽  
Author(s):  
S. V. Ponomareva ◽  
W. T. van Horssen
Keyword(s):  
Natural Frequencies ◽  
Dynamical Behavior ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Beam Model ◽  
Time Varying ◽  
Order Of Magnitude ◽  
Axially Moving ◽  
Transversal Vibrations ◽  
Initial Boundary Value

In this paper an initial-boundary value problem for a linear equation describing an axially moving stretched beam will be considered. The velocity of the beam is assumed to be time-varying. since the order of magnitude of the bending stiffness terms depends on the vibrations modes and the frequencies involved a that combination of two simplified models (a string equation and a beam with string effect equation) will be used to describe the transversal vibrations of the system accurately. Based on the calculations of the natural frequencies the regions of applicability of these models will be determined. A two time-scales perturbation method will be used to construct formal asymptotic approximations of the solutions. It will be shown that the linear axially moving “string to beam” model already has complicated dynamical behavior.

scholarly journals ON TRANSVERSAL VIBRATIONS OF AN AXIALLY MOVING BEAM UNDER INFLUENCE OF VISCOUS DAMPING

2020 ◽  
Vol 15 (11) ◽  
Author(s):  
Khalid H Malik
Keyword(s):  
Expansion Method ◽  
Conveyor Belt ◽  
Analytic Solutions ◽  
Axially Moving Beam ◽  
Viscous Damping ◽  
Damping Parameter ◽  
Moving Beam ◽  
Transversal Motion ◽  
Axially Moving ◽  
Transversal Vibrations

In this paper, a transversal vibration of an axially moving beam under the influence of viscous damping has been studied. The axial velocity of the beam is assumed to be positive, constant and small compared to wave-velocity. The beam is moving in a positive horizontal direction between the pair of pulleys and the length between the two pulleys is fixed. From a physical viewpoint, this model describes externally damped transversal motion for a conveyor belt system. The beam is assumed to be externally damped, where there is no restriction on the damping parameter which can be sufficiently large in contrast to much research material. The straightforward expansion method is applied to obtain approximated analytic solutions. It has been shown that the obtained solutions have not been broken out for any parametric values of the small parameter 𝜀. The constructed solutions are uniform and have been damped out. Even though there are several secular terms in the solutions, but they are small compared to damping.

scholarly journals On Travelling Wave Modes of Axially Moving String and Beam

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Lei Lu ◽  
Xiao-Dong Yang ◽  
Wei Zhang ◽  
Siu-Kai Lai
Keyword(s):  
Travelling Wave ◽  
Axially Moving Beam ◽  
Time Varying ◽  
Axially Moving String ◽  
Moving Beam ◽  
Axially Moving Beams ◽  
Axially Moving ◽  
Wave Phenomena ◽  
Moving Speed ◽  
Wave Modes

The traditional vibrational standing-wave modes of beams and strings show static overall contour with finite number of fixed nodes. The travelling wave modes are investigated in this study of axially moving string and beam although the solutions have been obtained in the literature. The travelling wave modes show time-varying contour instead of static contour. In the model of an axially moving string, only backward travelling wave modes are found and verified by experiments. Although there are n − 1 fixed nodes in the nth order mode, similar to the vibration of traditional static strings, the presence of travelling wave phenomenon is still spotted between any two adjacent nodes. In contrast to the stationary nodes of string modes, the occurrence of galloping nodes of axially moving beams is discovered: the nodes oscillate periodically during modal motions. Both forward and backward travelling wave phenomena are detected for the axially moving beam case. It is found that the ranges of forward travelling wave modes increase with the axially moving speed. It is also concluded that backward travelling wave modes can transform to the forward travelling wave modes as the transport speed surpasses the buckling critical speed.

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