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A Transmission Problem for Euler-Bernoulli beam with Kelvin-Voigt Damping |
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PP: 17-28 |
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Author(s) |
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C. A Raposo,
W. D. Bastos,
J. A. J. Avila,
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Abstract |
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| 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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