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A Lyapunov approach for the exponential stability of a damped Timoshenko beam

Abstract : In this technical note, we consider the stability properties of a viscously damped Timoshenko beam equation with spatially varying parameters. With the help of the port-Hamiltonian framework, we first prove the existence of solutions and show, by an appropriate Lyapunov function, that the system is exponentially stable and has an explicit decay rate. The explicit exponential bound is computed for an illustrative example of which we provide some numerical simulations.
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Preprints, Working Papers, ...
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https://hal-cnrs.archives-ouvertes.fr/hal-03790390
Contributor : Andrea Mattioni Connect in order to contact the contributor
Submitted on : Thursday, September 29, 2022 - 11:32:05 AM
Last modification on : Monday, October 3, 2022 - 10:13:54 AM

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  • HAL Id : hal-03790390, version 1
  • ARXIV : 2209.15281

Citation

Andrea Mattioni, Yongxin Wu, Yann Le Gorrec. A Lyapunov approach for the exponential stability of a damped Timoshenko beam. {date}. ⟨hal-03790390⟩

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