Stabilization of transverse vibrations of an inhomogeneous Euler- Bernoulli beam with a thermal effect

2015/06/04 by V. Octavio Vera, Octavio Vera V., Amélie Rambaud +5
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Stability and Controllability of Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.1506.01659

openalex publication_date 2015/06/04 · arxiv created 2015/06/05 · arxiv updated 2015/06/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We consider an inhomogeneous Euler-Bernoulli (EB) beam of length L clamped at both ends and subject to : an external frictional damping and a thermal effect (Fourier law). We prove the well-posedness of the model and analyze the behavior of the solution as t → + ∞. The existence is proved using semigroup theory, and the exponential stabilization of solutions is obtained considering multiplier technique. A numerical illustration of the energy decay is given, based on initial data close to a real physical experiment.

Citations

• Fundamentals of Vibrations

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