2007/10/03 by S.M. Shahruz, Shahram M. Shahruz, Shahruz, Shahram M.
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Dynamics and Control of Mechanical Systems #FOS: Mathematics #Fluid Dynamics and Vibration Analysis #Vibration and Dynamic Analysis #math.AP
paper · pdf · doi:10.48550/arxiv.0710.0872
15 pages. 1 figure
arxiv created 2007/10/03 · openalex publication_date 2007/10/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.