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

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

2007-10-03

arxiv.org/abs/0710.0872v1

Mathematics

Analysis of PDEs

15 pages. 1 figure

Scientific paper

In this paper, 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 function 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 and stabilization of strings with the Kelvin-Voigt damping are stated.

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