Long-time behaviour of a translational thermoelastic Timoshenko system with second sound

References

• Dadfarnia M, Jalili N, Xian B, et al. Lyapunov-based vibration control of translational Euler–Bernoulli beams using the stabilizing effect of beam damping mechanisms. J Vib Control. 2004;10:933–961.
   Web of Science ®Google Scholar
• Jalili N, Dadfarnia M, Hong F, et al. Adaptive non model-based piezoelectric control of flexible beams with translational base. Proceedings of the American Control Conference, Vol. 5; May 8–10; Anchorage, AK. 2002. p. 3802–3807.
   Google Scholar
• Zhu G, Ge SS, Lee TH. Variable structure regulation of a flexible arm with a translational base. Proceedings of the 36th Conference on Decision and Control, Vol. 2; San Diego, CA, USA. 1997. p. 1361–1366.
   Google Scholar
• Fernández Sare HD, Muñoz Rivera JE. On the stability of damped Timoshenko systems – Cattaneo versus Fourier law. Arch Ration Mech Anal. 2009;194(1):221–251.
   Web of Science ®Google Scholar
• Messaoudi S, Soufyane A. Boundary stabilization of solutions of a nonlinear system of Timoshenko type. Nonlinear Anal. 2007;67(7):2107–2121.
   Web of Science ®Google Scholar
• Ammar-Khodja F, Kerbal S, Soufyane A. Stabilization of the nonuniform Timoshenko beam. J Math Anal Appl. 2007;327(1):525–538.
   Web of Science ®Google Scholar
• Djebabla A, Tatar NE. Exponential stabilization of the Timoshenko system by a thermo-viscoelastic damping. J Dyn Control Syst. 2010;16(2):189–210.
   Web of Science ®Google Scholar
• Fernández Sare HD, Muñoz Rivera JE. Stability of Timoshenko systems with past history. J Math Anal Appl. 2008;339(1):482–502.
   Google Scholar
• Guesmia A, Messaoudi SA, Soufyane A. On the stabilization for a linear Timoshenko system with infinite history and applications to the coupled Timoshenko-heat systems. Electron J Differ Equ. 2012;2012:1–45.
   Web of Science ®Google Scholar
• Messaoudi S, Pokojovy M, Said-Houari B. Nonlinear damped Timoshenko systems with second sound – global existence and exponential stability. Math Methods Appl Sci. 2009;32(5):505–534.
   Google Scholar
• Messaoudi S, Said-Houari B. Energy decay in a Timoshenko-type system with history in thermoelasticity of type III. Adv Differ Equ. 2009;14(3–4):375–400.
   Web of Science ®Google Scholar
• Muñoz Rivera JE, Racke R. Mildly dissipative nonlinear Timoshenko systems: global existence and exponential stability. J Math Anal Appl. 2002;276(1):248–278.
   Web of Science ®Google Scholar
• Tatar NE. Exponential decay for a viscoelastically damped Timoshenko beam. Acta Math Sci Ser B Engl Ed. 2013;33(2):505–524.
   Google Scholar
• Tatar NE. Stabilization of a viscoelastic Timoshenko beam. Appl Anal. 2013;92(1):27–43.
   Web of Science ®Google Scholar
• Santos ML, Almeida Júnior DS, Muñoz Rivera JE. The stability number of the Timoshenko system with second sound. J Differ Equ. 2012;253(9):2715–2733.
   Web of Science ®Google Scholar
• Apalara T, Messaoudi S, Keddi A. On the decay rates of Timoshenko system with second sound. Math Methods Appl Sci. 2016;39:2671–2684.
   Web of Science ®Google Scholar
• Berkani A, Tatar NE. Stabilization of a viscoelastic Timoshenko beam fixed in to a moving base. Math Modell Nat Phenom. 2019;14(5):Article number 501, 29 pages.
   Google Scholar
• Berkani A, Tatar NE, Kelleche A. Vibration control of a viscoelastic translational Euler-Bernoulli beam. J Dyn Control Syst. 2018;24(1):167–199.
   Google Scholar
• Berkani A, Tatar NE, Khemmoudj A. Control of a viscoelastic translational Euler–Bernoulli beam. Math Methods Appl Sci. 2017;40(1):237–254.
   Web of Science ®Google Scholar
• Kafini M, Tatar NE. Control of a thermo-viscoelastic translational Timoshenko beam. Int J Control. 2021;94(8):2161–2174. doi:10.1080/00207179.2019.1695146
   Google Scholar
• Shi DH, Hou SH, Feng DX. Feedback stabilization of a Timoshenko beam with an end mass. Int J Control. 1998;69(2):285–300.
   Web of Science ®Google Scholar
• Neves AF, Ribeiro HS, Lopes O. On the spectrum of evolution operators generated by hyperbolic systems. J Funct Anal. 1986;67:320–344.
   Web of Science ®Google Scholar