Publication Cover
Applicable Analysis
An International Journal
Volume 102, 2023 - Issue 16
86
Views
5
CrossRef citations to date
0
Altmetric
Research Article

Stabilization of laminated beam with structural damping and a heat conduction of Gurtin–Pipkin's law

ORCID Icon
Pages 4659-4677 | Received 08 Apr 2022, Accepted 23 Sep 2022, Published online: 08 Oct 2022

References

  • Dridi H, Feng B, Zennir K. Stability of Timoshenko system coupled with thermal law of Gurtin–Pipkin affecting on shear force. Appl Anal. 2021;101:5171–5192. https://doi.org/10.1080/00036811.2021.1883591.
  • Hansen SW, Spies RD. Structural damping in laminated beams due to interfacial slip. J Sound Vibration. 1997;204(2):183–202.
  • Alves MS, Monteiro RN. Exponential stability of laminated Timoshenko beams with boundary/internal controls. J Math Anal Appl. 2020;482(1):1–16.
  • Apalara TA, Nass AM, Al Sulaimani H. On a laminated timoshenko beam with nonlinear structural damping. Math Comput Appl. 2020;25(2):35.
  • Apalara TA, Raposo CA, Nonato CAS. Exponential stability for laminated beams with a frictional damping. Archiv Der Mathematik. 2020;114(4):471–480.
  • Apalara TA. Exponential stability of laminated beams with interfacial slip. Mechan Solids. 2021;56(1):131–137.
  • Feng B. Well-posedness and exponential decay for laminated timoshenko beams with time delays and boundary feedbacks. Math Meth Appl Sci. 2018;41(3):1162–1174.
  • Feng B, Almeida Júnior DS, Ramos AJA. Exponential stabilization of laminated beams with history memories. Math Nachrichten. 2021;294(3):559–579.
  • Lo A, Tatar NE. Stabilization of laminated beams with interfacial slip. Electron J Differ Equations. 2015;2015(129):1–14.
  • Lo A, Tatar NE. Uniform stability of a laminated beam with structural memory. Qual Theory Dyn Syst. 2016;15(2):517–540.
  • Lo A, Tatar NE. Exponential stabilization of a structure with interfacial slip. Discrete Contin Dyn Syst. 2016;36(11):6285–6306.
  • Mustafa MI. On the stabilization of viscoelastic laminated beams with interfacial slip. Z Angew Math Phys. 2018;69(2):1–14.
  • Mustafa MI. Boundary control of laminated beams with interfacial slip. J Math Phys. 2018;59(5):1–9.
  • Tatar NE. Stabilization of a laminated beam with interfacial slip by boundary controls. Bound Value Probl. 2015;2015:1–11.
  • Wang JM, Xu GQ, Yung SP. Exponential stabilization of laminated beams with structural damping and boundary feedback controls. SIAM J Control Optim. 2005;44(5):1575–1597.
  • Liu W, Zhao W. Stabilization of a thermoelastic laminated beam with past history. Appl Math Optim. 2019;80(1):103–133.
  • Mukiawa SE, Apalara TA, Messaoudi SA. A general and optimal stability result for a laminated beam. J Integ Equ Appl. 2020;32(3):341–359.
  • Djellali F. Well posedness and stability result for a thermoelastic laminated beam with structural damping. Ricerche Mat. 2022:1–25. https://doi.org/10.1007/s11587-022-00708-2.
  • Feng B. On a thermoelastic laminated Timoshenko beam: well posedness and stability. Complexity. 2021;2020:1–13. https://doi.org/10.1155/2020/5139419.
  • Apalara TA. Uniform stability of a laminated beam with structural damping and second sound. Z Angew Math Phys. 2017;68(2):1–16.
  • Mukiawa SE, Apalara TA, Messaoudi SA. A stability result for a memory-type laminated-thermoelastic system with Maxwell-Cattaneo heat conduction. J Thermal Stresses. 2020;43(11):1437–1466.
  • Liu W, Zhao W. On the stability of a laminated beam with structural damping and Gurtin–Pipkin thermal law. Nonlinear Anal Modell Control. 2021;26(3):396–418.
  • Dell'Oro F, Pata V. On the stability of Timoshenko systems with Gurtin–Pipkin thermal law. J Differ Equations. 2014;257(2):523–548.
  • Dell'Oro F. Asymptotic stability of thermoelastic systems of Bresse type. J Differ Equations. 2015;258(11):3902–3927.
  • Apalara TA. On the stability of a thermoelastic laminated beam. Acta Math Scientia. 2019;39(6):1517–1524.
  • Liu W, Luan Y, Liu Y, et al. Well-posedness and asymptotic stability to a laminated beam in thermoelasticity of type III. Math Meth Appl Sci. 2020;43(6):3148–3166.
  • Liu W, Zhao W. Exponential and polynomial decay for a laminated beam with Fourier's law of heat conduction and possible absence of structural damping. Front Math China. 2021;16(4):997–1021.
  • Nonato C, Raposo C, Feng B. Exponential stability for a thermoelastic laminated beam with nonlinear weights and time-varying delay. Asymptotic Anal. 2022;126(1-2):157–185.
  • Fareh A. Exponential stability of a porous thermoelastic system with Gurtin–Pipkin thermal law. RACSAM. 2022;116(1):1–19. https://doi.org/10.1007/s13398-021-01132-1.
  • Grasselli M, Pata V. Uniform attractors of nonautonomous dynamical systems with memory. In: Lorenzi A, Ruf B, editors. Evolution equations, semigroups and functional analysis. Basel: Birkhäuser; 2002. p. 155–178. (Progress in Nonlinear Differential Equations and Their Applications; vol. 50).
  • Dafermos CM. Asymptotic stability in viscoelasticity. Arch Rational Mech Anal. 1970;37(4):297–308.
  • Pazy A. Semigroups of linear operators and applications to partial differential equations. Vol. 44. New York: Springer-Verlag; 1983.
  • Zelati MC, Dell'Oro F, Pata V. Energy decay of type III linear thermoelastic plates with memory. J Math Anal Appl. 2013;401(1):357–366.
  • Muñoz Rivera JE, Racke R. Mildly dissipative nonlinear Timoshenko systems–global existence and exponential stability. J Math Anal Appl. 2002;276(1):248–278.
  • Gearhart L. Spectral theory for contraction semigroups on Hilbert space. Trans Am Math Soc. 1978;236:385–394.
  • Huang F. Characteristic conditions for exponential stability of linear dynamical systems in Hilbert spaces. Ann Differ Equations. 1985;1:43–56.
  • Prüss J. On the spectrum of C0-semigroups. Trans Am Math Soc. 1984;284(2):847–857.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.