88
Views
8
CrossRef citations to date
0
Altmetric
Articles

Memory response in plane wave reflection in generalized magneto-thermoelasticity

, ORCID Icon & ORCID Icon
Pages 1354-1374 | Received 09 Feb 2019, Accepted 10 Apr 2019, Published online: 22 Apr 2019

References

  • Eringen AC. Nonlocal continum field theories. New York: Springer; 2002.
  • Biot M. Thermoelasticity and irreversible thermodynamics. J Appl Phys. 1956;27:240–53. doi: 10.1063/1.1722351
  • Cattaneo C. Sur une forme de l equation de la chaleur eliminant le paradoxe d ure propagation instantaneee [On a form of the heat equation eliminating the paradox of the instantaneous spread]. [In French.] Comptes Rendus Acad Sci. 1958;2(47):431–433.
  • Lord HW, Shulman Y. A generalized dynamical theory of thermoelasticity. J Mech Phys Solids. 1967;15:299–309. doi: 10.1016/0022-5096(67)90024-5
  • Green AE, Lindsay KA. Thermoelasticity. J Elasticity. 1971;2:1–7. doi: 10.1007/BF00045689
  • Green AE, Naghdi PM. A re-examination of the basic postulates of thermomechanics. Proc R Soc London Ser. 1992;432(1885):171–194. doi: 10.1098/rspa.1991.0012
  • Wilson AJ. The propagation of magneto-thermoelastic plane waves. Proc Camb Philos Soc. 1963;59:438–488.
  • Parkus H. Electromagnetic interactions in elastic solids. 257. Vienna: Springer-Verlag; 1979. CISM courses and lectures.
  • Paria G. On magneto-thermo-elastic plane waves. Proc Camb Philos Soc. 1962;58:527–531. doi: 10.1017/S030500410003680X
  • Nayfeh AH, Nemat-Nasser S. Electromagneto-thermoelastic plane waves in solids with thermal relaxation. J Appl Mech. 1972;39:108–113. doi: 10.1115/1.3422596
  • Agarwal VK. On electromagneto-thermoelastic plane waves. Acta Mech. 1979;34:181–191. doi: 10.1007/BF01227983
  • Roychoudhuri SK. Electro-magneto-thermo-elastic plane waves in rotating media with thermal relaxation. Int J Eng Sci. 1984;22:519–530. doi: 10.1016/0020-7225(84)90054-5
  • Abd-Alla AN, Yahia AA, Abo-Dahab SM. On the reflection of the generalized magneto-thermo-viscoelastic plane waves. Chaos Solitons Fractals. 2003;16:211–231. doi: 10.1016/S0960-0779(02)00170-4
  • Roy Choudhuri SK, Banerjee M. Magneto-viscoelastic plane waves in rotating media in the generalized thermoelasticity II. Int J Math Math Sci. 2005;11:1819–1834. doi: 10.1155/IJMMS.2005.1819
  • Othman MIA, Song Y. The effect of rotation on the reflection of magneto-thermoelastic waves under thermoelasticity without energy dissipation. Acta Mech. 2006;184:189–204. doi: 10.1007/s00707-006-0337-4
  • Othman MIA, Song Y. Reflection of magneto-thermoelastic waves with two relaxation times and temperature dependent elastic moduli. Appl Math Model. 2008;32:483–500. doi: 10.1016/j.apm.2007.01.001
  • Abo-Dahab SM, Mohamed RA, Singh B. Rotation and magnetic field effects on P wave reflection from a stress-free surface of elastic half-space with voids under one thermal relaxation time. J Vib Control. 2011;17:1827–1839. doi: 10.1177/1077546310371491
  • Allam MNM, Rida SZ, Abo-Dahab SM, et al. GL model on reflection of P and SV-waves from the free surface of thermoelastic diffusion solid under influence of the electromagnetic field and initial stress. J Thermal Stresses. 2014;37:471–487. doi: 10.1080/01495739.2013.870861
  • Abd-Alla AM, Othman MIA, Abo-Dahab SM. Reflection of plane waves from electro-magneto-thermoelastic half-space with a dual-phase-lag model. Comput Mater Contin. 2016;51:63–79.
  • Abo-Dahab SM, Abd-Alla AM, Elsagheer M, Effect of rotation and gravity on the reflection of P-waves from thermo- magneto-microstretch medium in the context of three phase lag model with initial stress. Microsyst Technol. 2018;24:3357–3369. doi: 10.1007/s00542-017-3697-x
  • Wang J-L, Li H-F. Surpassing the fractional derivative: concept of the memory-dependent derivative. Comput Math Appl. 2011;62:1562–1567. doi: 10.1016/j.camwa.2011.04.028
  • Ezzat MA, El-Karamany AS, El-Bary AA. A novel magneto-thermoelasticity theory with memory-dependent derivative. J Electromagn Waves Appl. 2015;29:1018–1031. doi: 10.1080/09205071.2015.1027795
  • Mainardi F. Fractional calculus and waves in linear viscoelasticity. London: Imperial College Press; 2010.
  • Rossikhin YA, Shitikova MV. Application of fractional calculus for dynamic problems of solid mechanics: novel trends and recent results. Appl Mech Rev. 2011;63(1):1562–1567. Available from: https://doi.org/10.1115/1.4000563
  • Stiassnie M. On the application of fractional calculus for formulation of viscoelastic model. Appl Math Model. 1979;3(4):300–302. doi: 10.1016/S0307-904X(79)80063-3
  • Ezzat MA, El-Karamany AS, El-Bary AA. Generalized thermo-viscoelasticity with memory-dependent derivatives. Int J Mech Sci. 2014;89:470–475. doi: 10.1016/j.ijmecsci.2014.10.006
  • Sarkar N, Ghosh D, Lahiri A. A two-dimensional magneto-thermoelastic problem based on a new two-temperature generalized thermoelasticity model with memory-dependent derivative. Mech Adv Mater Struct. 2018. doi:10.1080/15376494.2018.1432784.
  • Gorenflo R, Mainardi F. Fractional calculus: integral and differential equations of fractional orders, fractals and fractional calculus in continuum mechanics. Wien: Springer; 1997.
  • Atanackovic TM, Pilipovic S, Stankovic B, et al. Fractional calculus with application in mechanics. London: Wiley; 2014.
  • Diethelm K. Analysis of fractional differential equation: an application oriented exposition using differential operators of caputo type. Berlin: Springer; 2010.
  • Sherief HH, El-Sayed A, El-Latief A. Fractional order theory of thermoelasticity. Int J Solids Struct. 2010;47:269–275. doi: 10.1016/j.ijsolstr.2009.09.034
  • Youssef H. Theory of fractional order generalized thermoelasticity. J Heat Trans. 2010;132. doi: 10.1115/1.4000705
  • Ezzat MA, Fayik MA. Fractional order theory of thermoelastic diffusion. J Thermal Stresses. 2011;34:851–872. doi: 10.1080/01495739.2011.586274
  • Yu Y-J, Hu W, Tian X-G. A novel generalized thermoelasticity model based on memory-dependent derivative. Int J Eng Sci. 2014;81:123–134. doi: 10.1016/j.ijengsci.2014.04.014
  • Ezzat MA, Youssef HM. Three-dimensional thermal shock problem of generalized thermoelastic half-space. Appl Math Model. 2010;34:3608–3622. doi: 10.1016/j.apm.2010.03.010
  • Chandrasekharaiah DS. Thermoelastic plane waves withour energy dissipation. Mech Res Commun. 1996;23:549–555. doi: 10.1016/0093-6413(96)00056-0
  • Billingham J, King AC. Wave motion. New York: Cambridge University Press; 2001.
  • Sharma JN, Grover D, Kaur D. Mathematical modelling and analysis of bulk waves in rotating generalized thermoelastic media with voids. Appl Math Model. 2011;35:3396–3407. doi: 10.1016/j.apm.2011.01.014
  • Achenbach JD. Wave propagation in elastic solids. New York: North-Holland; 1976.

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.