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

[+] Author Affiliations
S. V. Ponomareva, W. T. van Horssen

Delft University of Technology, Delft, The Netherlands

Paper No. DETC2007-34363, pp. 801-807; 7 pages
doi:10.1115/DETC2007-34363
From:
  • ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 5: 6th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C
  • Las Vegas, Nevada, USA, September 4–7, 2007
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 0-7918-4806-X | eISBN: 0-7918-3806-4
  • Copyright © 2007 by ASME

abstract

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.

Copyright © 2007 by ASME
Topics: String , Vibration

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