A Transmission Problem for Euler-Bernoulli beam with Kelvin-Voigt Damping
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Undergraduate course
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Natural Sciences Publishing Corporation
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Article
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Abstract
In this work we consider a transmission problem for the longitudinal displacement of a Euler-Bernoulli beam, where one small part of the beam is made of a viscoelastic material with Kelvin-Voigt constitutive relation. We use semigroup theory to prove existence and uniqueness of solutions. We apply a general results due to L. Gearhart [5] and J. Pruss [10] in the study of asymptotic behavior of solutions and prove that the semigroup associated to the system is exponentially stable. A numerical scheme is presented,
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Keywords
Transmission problem, Exponencial stability, Euler-Bernoulli beam, Kelvin-Voigt damping, Semigroup, Numerical scheme
Language
English
Citation
Applied Mathematics & Information Sciences. Kalamazoo: Natural Sciences Publishing Corporation, v. 5, n. 1, p. 17-28, 2011.
