Stability of an N-component Timoshenko beam with localized Kelvin-Voigt and frictional dissipation

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dc.contributor.authorMaryati, Tita K.
dc.contributor.authorMunoz Rivera, Jaime E.
dc.contributor.authorRambaud, Amelie
dc.contributor.authorVera, Octavio
dc.date.accessioned2022-02-16T17:41:22Z
dc.date.available2022-02-16T17:41:22Z
dc.date.issued2018-07-01
dc.description.abstractWe 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.
dc.description.departmentMathematics
dc.formatText
dc.format.extent18 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationMaryati, 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.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/15336
dc.language.isoen
dc.publisherTexas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2018, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectTimoshenko's model
dc.subjectBeam equation
dc.subjectLocalized dissipation
dc.subjectViscoelaticity
dc.subjectLack of exponential stability
dc.subjectExponential and polynomial stability
dc.titleStability of an N-component Timoshenko beam with localized Kelvin-Voigt and frictional dissipation
dc.typeArticle

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