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Technical Briefs

Stability of a Nonlinear Axially Moving String With the Kelvin–Voigt Damping

[+] Author and Article Information
S. M. Shahruz1

 Berkeley Engineering Research Institute, P.O. Box 9984, Berkeley, CA 94709shahruz@cal.berkeley.edu

1

Corresponding author.

J. Vib. Acoust 131(1), 014501 (Jan 07, 2009) (4 pages) doi:10.1115/1.3025835 History: Received October 03, 2007; Revised August 15, 2008; Published January 07, 2009

In this note, a nonlinear axially moving string with the Kelvin–Voigt damping is considered. It is proved that the string is stable, i.e., its transversal displacement converges to zero when the axial speed of the string is less than a certain critical value. The proof is established by showing that a Lyapunov functional corresponding to the string decays to zero exponentially. It is also shown that the string displacement is bounded when a bounded distributed force is applied to it transversally. Furthermore, a few open problems regarding the stability of strings with the Kelvin–Voigt damping are stated.

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Copyright © 2009 by American Society of Mechanical Engineers
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References

Figures

Grahic Jump Location
Figure 1

A stringlike continuum is pulled at a constant speed through two fixed eyelets. The distance between the eyelets is 1.

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