Stability of an N-component Timoshenko beam with localized Kelvin-Voigt and frictional dissipation
Date
2018-07-01
Authors
Maryati, Tita K.
Munoz Rivera, Jaime E.
Rambaud, Amelie
Vera, Octavio
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We consider the transmission problem of a Timoshenko's beam composed by N components, each of them being either purely elastic, or a Kelvin-Voigt viscoelastic material, or an elastic material inserted with a frictional damping mechanism. Our main result is that the rate of decay depends on the position of each component. More precisely, we prove that the Timoshenko's model is exponentially stable if and only if all the elastic components are connected with one component with frictional damping. Otherwise, there is no exponential stability, but a polynomial decay of the energy as as 1/t2. We introduce a new criterion to show the lack of exponential stability, Theorem 1.2. We also consider the semilinear problem.
Description
Keywords
Timoshenko's model, Beam equation, Localized dissipation, Viscoelaticity, Lack of exponential stability, Exponential and polynomial stability
Citation
Maryati, T. K., Muñoz Rivera, J. E., Rambaud, A., & Vera, O. (2018). Stability of an N-component Timoshenko beam with localized Kelvin-Voigt and frictional dissipation. <i>Electronic Journal of Differential Equations, 2018</i>(136), pp. 1-18.
Rights
Attribution 4.0 International