Abstract
This manuscript deals with a thermo-viscoelastic system describing the vibrations of a flexible structure. We study this structure's stabilization problem when subjected to Kelvin-Voigt damping and the second sound. Cattaneo-Vernotte's law governs the thermal effect, eliminating the physical paradox of equal speed of waves in the classical thermoelastic theory. Semigroup theory proves the solution's existence and uniqueness. Exponential stability is proved by the energy method.
Publisher
Department of Library and Documentation, Mersin University
Reference27 articles.
1. R. A. Adams, Sobolev Spaces, Academic Press, New York, (1975).
2. M. Alves, P. Gamboa, G. Gorain, A. Rambaud, O. Vera, Asymptotic behavior of a flexible structure with Cattaneo type of thermal effect, Indag. Math. 27 (2016), 821–834, https://doi.org/10.1016/j.indag.2016.03.001.
3. J. L. Auriault, Cattaneo-Vernotte equation versus Fourier thermoelastic hyperbolic heat equation, Int. J. Eng. Sci. 101 (2016), 45–49. https://doi.org/10.1016/j.ijengsci.2015.12.002.
4. H. T. Banks, R. C. Smith, Y. Wang, Smart Material Structures: Modeling, Estimation, and Control, Wiley, London, (1996).
5. D. S. Chandrasekharaiah, Hyperbolic thermoelasticity: A review of recent literature Appl. Mech. Rev. 51 (1998), 705–728, https://doi.org/10.1115/1.3098984.