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

Octavio Vera V.; Amelie Rambaud; Roberto Rozas

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arXiv · 1506.01659

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

Octavio Vera V.·Amelie Rambaud·Roberto Rozas

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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 $t \rightarrow + \infty.$ 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.

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Octavio Vera V., Amelie Rambaud, Roberto Rozas. 2015-06-04. Stabilization of transverse vibrations of an inhomogeneous Euler- Bernoulli beam with a thermal effect. https://arxiv.org/abs/1506.01659

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