Publication Cover
Applicable Analysis
An International Journal
Volume 100, 2021 - Issue 2
71
Views
0
CrossRef citations to date
0
Altmetric
Articles

On a model for the magnetoelastic vibrations of a perfectly conducting Mindlin–Timoshenko plate

Pages 322-334 | Received 04 Dec 2018, Accepted 29 Mar 2019, Published online: 12 Apr 2019

References

  • Loredo A. A multilayered plate theory with transverse shear effects and normal warping functions. Compos Struct. 2016;156:361–374. doi: 10.1016/j.compstruct.2015.08.084
  • Grobbelaar-Van Dalsen M. Dynamic boundary stabilization of a Reissner– Mindlin plate with Timoshenko beam. Math Meth Appl Sci. 2004;27:1301–1315. doi: 10.1002/mma.506
  • Grobbelaar-Van Dalsen M. On a structural acoustic model with interface a Reissner–Mindlin plate or a Timoshenko beam. J Math Anal Appl. 2006;320:121–144. doi: 10.1016/j.jmaa.2005.06.034
  • Fernández Sare HD. On the stability of Mindlin–Timoshenko plates. Quart Appl Math. 2009;67(2):249–263. doi: 10.1090/S0033-569X-09-01110-2
  • Grobbelaar-Van Dalsen M. Stabilization of a thermoelastic Mindlin–Timoshenko plate model revisited. Z Angew Math Phys. 2013;64:1305–1325. doi: 10.1007/s00033-012-0289-6
  • Grobbelaar-Van Dalsen M. Polynomial decay rates of a thermoelastic Mindlin–Timoshenko plate model with Dirichlet boundary conditions. Z Angew Math Phys. 2015;66:113–128. doi: 10.1007/s00033-013-0391-4
  • Pokojovy M. On stability of hyperbolic thermoelastic Reissner–Mindlin Timoshenko plates. Math Meth Appl Sci. 2015;38:1225–1246. doi: 10.1002/mma.3140
  • Grobbelaar-Van Dalsen M. On the dissipative effect of a magnetic field in a Mindlin–Timoshenko plate model. Z Angew Math Phys. 2012;63:1047–1065. doi: 10.1007/s00033-012-0206-z
  • Perla Menzala G, Zuazua E. Energy decay of magnetoelastic waves in a bounded conductive medium. Asymptot Anal. 1998;18:349–362.
  • Sermange M, Temam R. Some mathematical questions related to the MHD equations. Comm Pure Appl Math. 1983;36:635–664. doi: 10.1002/cpa.3160360506
  • Grobbelaar-Van Dalsen M. Correction to: on the dissipative effect of a magnetic field in a Mindlin–Timoshenko plate model. Z Angew Math Phys. 2017;68:124. doi: 10.1007/s00033-017-0873-x
  • Ferreira MV, Muñoz Rivera JE. Polynomial stability of a magneto-thermoelastic Mindlin–Timoshenko plate model. Z Angew Math Phys. 2018;69:010001-16.
  • Grobbelaar-Van Dalsen M. Exponential stabilization of magnetoelastic waves in a Mindlin–Timoshenko plate by localized internal damping. Z Angew Math Phys. 2015;66:1761–1776.
  • Grobbelaar-Van Dalsen M. An analytic semigroup for the magnetoelastic Mindlin–Timoshenko plate model. Appl Anal. 2017;96:886–896. doi: 10.1080/00036811.2016.1167189
  • Karličić D, Murmu T, Cajić M, et al. Dynamics of multiple viscoelastic carbon nanotube based nanocomposites with axial magnetic field. J App Phys. 2014;115:234303. doi: 10.1063/1.4883194
  • Pazy A. Semigroups of linear operators and applications to partial differential equations. New York: Springer–Verlag; 1983. (Applied Mathematical Sciences).
  • Phillips RS. Perturbation theory for semigroups of linear operators. Trans Amer Math Soc. 1953;74:199–221. doi: 10.1090/S0002-9947-1953-0054167-3
  • Borichev A, Tomilov Y. Optimal polynomial decay rate of functions and operator semigroups. Math Ann. 2010;347:455–478. doi: 10.1007/s00208-009-0439-0
  • Hai PN. On the the polynomial stability of evolution families. Appl Anal. 2016;95:1239–1255. doi: 10.1080/00036811.2015.1058364
  • Nicaise S. Internal stabilization of a Mindlin–Timoshenko model by interior feedbacks. Math Control Relat Fields. 2011;1:331–352. doi: 10.3934/mcrf.2011.1.331
  • Jorge Silva MA, Ma TF, Munöz Rivera JE. Mindlin–Timoshenko systems with Kelvin–Voigt: analyticity and optimal decay rates. J Math Anal Appl. 2014;117:164–179. doi: 10.1016/j.jmaa.2014.02.066
  • Tebou L. Indirect stabilization of a Mindlin–Timoshenko plate. J Math Anal Appl. 2017;449:1880–1891. doi: 10.1016/j.jmaa.2017.01.015

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.