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<p>In this paper, we investigate the Timoshenko suspended-beam system with thermal and mass diffusion effects. The beam undergoes heat and mass exchange with the environment during thermodiffusion. Using semigroup theory, we establish the well-posedness of the problem and we prove the exponential decay property of the solutions by introducing a suitable Lyapunov functional. Moreover, we introduce a numerical approximation combining implicit Euler method in time and finite element method in space and we prove that the associated discrete energy decays. Then, we present a priori error estimates from which the linear convergence of the algorithm is derived under suitable regularity conditions. Finally, numerical simulations are performed to validate the accuracy and energy stability of the proposed scheme.</p>

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Stability and Numerical Results for a Suspension Bridge with Thermodiffusion Effects

  • 期刊论文

  • 发表日期：

    2025年12月22日

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  • My Driss Aouragh,
  • Mustapha El Baz,
  • M’hamed Segaoui

摘要

In this paper, we investigate the Timoshenko suspended-beam system with thermal and mass diffusion effects. The beam undergoes heat and mass exchange with the environment during thermodiffusion. Using semigroup theory, we establish the well-posedness of the problem and we prove the exponential decay property of the solutions by introducing a suitable Lyapunov functional. Moreover, we introduce a numerical approximation combining implicit Euler method in time and finite element method in space and we prove that the associated discrete energy decays. Then, we present a priori error estimates from which the linear convergence of the algorithm is derived under suitable regularity conditions. Finally, numerical simulations are performed to validate the accuracy and energy stability of the proposed scheme.