Stability of a Timoshenko System with Localized Kelvin–Voigt Dissipation

We consider the Timoshenko beam with localized Kelvin–Voigt dissipation distributed over two components: one of them with constitutive law of the type C 1 , and the other with discontinuous law. The third component is simply elastic, where the viscosity is not effective. Our main result is that the...

Full description

Saved in:
Bibliographic Details
Published inApplied mathematics & optimization Vol. 84; no. 3; pp. 3547 - 3563
Main Authors Aguilera Contreras, Gabriel, Muñoz Rivera, Jaime E.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.12.2021
Springer Nature B.V
Subjects
Applied mathematics
Calculus of Variations and Optimal Control; Optimization
Control
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Optimization
Simulation
Systems Theory
Theoretical
Timoshenko beams
Viscoelasticity
Localized viscoelastic dissipative mechanism
Transmission problem
35P05
Polynomial decay
Timoshenko beam
35B40
35Q74
Exponential stability
Online AccessGet full text

Cover

More Information
Summary:We consider the Timoshenko beam with localized Kelvin–Voigt dissipation distributed over two components: one of them with constitutive law of the type C 1 , and the other with discontinuous law. The third component is simply elastic, where the viscosity is not effective. Our main result is that the decay depends on the position of the components. We will show that the system is exponentially stable if and only if the component with discontinuous constitutive law is not in the center of the beam. When the discontinuous component is in the middle, the solution decays polynomially.
ISSN:0095-4616
1432-0606
DOI:10.1007/s00245-021-09758-8