On the transversal vibrations of a conveyor belt with a low and time-varying velocity. Part I: the string-like case

2003 ◽  
Vol 264 (1) ◽  
pp. 117-133 ◽  
Author(s):  
G. Suweken ◽  
W.T. Van Horssen
Keyword(s):  
Conveyor Belt ◽  
Time Varying ◽  
Transversal Vibrations

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.

On the Transversal Vibrations of a Conveyor Belt Using a String-Like Equation

2001 ◽  
Author(s):  
Gede Suweken ◽  
W. T. van Horssen
Keyword(s):  
Wave Speed ◽  
Dynamical Behavior ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Conveyor Belt ◽  
Linear Wave ◽  
Long Time ◽  
Vertical Vibrations ◽  
Transversal Vibrations ◽  
Initial Boundary Value

Abstract In this paper an initial-boundary value problem for a linear wave (string) equation is considered. This problem can be used as a simple model to describe the vertical vibrations of a conveyor belt, for which the velocity is small with respect to the wave speed. In this paper the belt is assumed to move with varying speed. Formal asymptotic approximations of the solutions are constructed to show the complicated dynamical behavior of the conveyor belt. It also will be shown that for this problem, the truncation method is not valid on long time scales.

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.

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