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

2022/09/30 by Andrea Mattioni, Yongxin Wu, Mattioni, Andrea +3
Engineering · Mathematics · #Control and Stability of Dynamical Systems #FOS: Mathematics #Numerical methods for differential equations #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations

paper · doi:10.48550/arxiv.2209.15281

openalex publication_date 2022/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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