Reflection of magneto-thermoelastic waves at a solid half-space under modified Green–Lindsay model with two temperatures

References

• M. Biot, “Thermoelasticity and irreversible thermodynamics,” J. Appl. Phys., vol. 27, no. 3, pp. 240–253, 1956. DOI: 10.1063/1.1722351.
   Web of Science ®Google Scholar
• H. W. Lord and Y. Shulman, “A generalized dynamical theory of thermoelasticity,” J. Mech. Phys. Solids, vol. 15, no. 5, pp. 299–309, 1967. DOI: 10.1016/0022-5096(67)90024-5.
   Web of Science ®Google Scholar
• C. Cattaneo, “Sur une forme de l’equation de la chaleur eliminant le paradoxe d’ure propagation instantaneee,” Comptes. Rendus. Acad. Sci, vol. 2, pp. 431–433, 1958. [On a form of the heat equation eliminating the paradox of the instantaneous spread]. [In French].
   Google Scholar
• A. E. Green and K. A. Lindsay, “Thermoelasticity,” J. Elast., vol. 2, no. 1, pp. 1–7, 1972. DOI: 10.1007/BF00045689.
   Google Scholar
• Y. J. Yu, Z.-N. Xue, and X.-G. Tian, “A modified Green-Lindsay thermoelastidcity with strain rate to eliminate discontinuity,” Meccanica, vol. 53, no. 10, pp. 2543–2554, 2018. DOI: 10.1007/s11012-018-0843-1.
   Web of Science ®Google Scholar
• A. E. Green and P. M. Naghdi, “On undamped heat waves in an elastic solid,” J. Therm. Stresses, vol. 15, no. 2, pp. 253–264, 1992. DOI: 10.1080/01495739208946136.
   Web of Science ®Google Scholar
• A. E. Green and P. M. Naghdi, “Thermoelasticity without energy disspation,” J. Elast., vol. 31, no. 3, pp. 189–208, 1993. DOI: 10.1007/BF00044969.
   Web of Science ®Google Scholar
• R. Quintanilla, “Some qualitative results for a modification of the Green-Lindsay thermoelasticity,” Meccanica, vol. 53, no. 14, pp. 3607–3613, 2018. DOI: 10.1007/s11012-018-0889-0.
   Web of Science ®Google Scholar
• P. J. Chen and M. E. Gurtin, “On a theory of heat conduction involving two temperatures,” J. Appl. Math. Phys., vol. 19, no. 4, pp. 614–627, 1968. DOI: 10.1007/BF01594969.
   Web of Science ®Google Scholar
• P. J. Chen, M. E. Gurtin, and W. O. Williams, “A note on non-simple heat conduction,” J. Appl. Math. Phys., vol. 19, no. 6, pp. 969–970, 1968. DOI: 10.1007/BF01602278.
   Web of Science ®Google Scholar
• P. J. Chen, M. E. Gurtin, and W. O. Williams, “On the thermodynamics of non-simple elastic materials with two temperatures,” J. Appl. Math. Phys., vol. 20, no. 1, pp. 107–112, 1969. DOI: 10.1007/BF01591120.
   Web of Science ®Google Scholar
• R. Quintanilla and P. M. Jordan, “A note on the two temperature theory with dual-phase-lag delay: Some exact solutions,” Mech. Res. Commun., vol. 36, no. 7, pp. 796–803, 2009. DOI: 10.1016/j.mechrescom.2009.05.002.
   Web of Science ®Google Scholar
• R. Quintanilla, “On existence, structural stability, convergence and spatial behavior in thermoelasticity with two temperatures,” Acta Mech., vol. 168, no. 1/2, pp. 61–73, 2004. DOI: 10.1007/s00707-004-0073-6.
   Web of Science ®Google Scholar
• R. Quintanilla, “Exponential stability and uniqueness in thermoelasticity with two temperatures,” Dyn. Cont. Discrete Impul. Sys. A, vol. 11, pp. 57–68, 2004.
   Web of Science ®Google Scholar
• R. Quintanilla de Latorre and R. Racke, “Stability for thermoelastic plates with two temperatures. Discrete and continuous dynamical systems,” Series A, vol. 37, no. 12, pp. 6333–6352, 2017.
   Google Scholar
• H. M. Youssef, “Theory of two temperatures-generalized thermoelasticity,” IMA J. Appl. Math., vol. 71, no. 3, pp. 383–390, 2006. DOI: 10.1093/imamat/hxh101.
   Web of Science ®Google Scholar
• S. Y. Atwa, “Generalized magneto-thermoelasticity with two temperature and initial stress under Green–Naghdi theory,” Appl. Math. Model., vol. 38, no. 21/22, pp. 5217–5230, 2014. DOI: 10.1016/j.apm.2014.04.023.
   Web of Science ®Google Scholar
• K. Lotfy, “Two temperature generalized magneto-thermoelastic interactions in an elastic medium under three theories,” Appl. Math. Comp., vol. 227, pp. 871–888, 2014. DOI: 10.1016/j.amc.2013.11.063.
   Web of Science ®Google Scholar
• S. M. Abo-Dahab, “A two-temperature generalized magneto-thermoelasticformulation for a rotating medium with thermal shockunder hydrostatic initial stress,” Cont. Mech. Therm., 2019. DOI: 10.1007/s00161-019-00765-3.
   Web of Science ®Google Scholar
• N. Sarkar and S. Mondal, “Transient responses in a two temperatures thermoelastic infinite medium having cylindrical cavity due to moving heat source with memory-dependent derivative,” Z. Angew. Math. Mech., vol. 99, no. 6, pp. e201800343, 2019. DOI: 10.1002/zamm.201800343.
   Web of Science ®Google Scholar
• S. Mondal, A. Sur, and M. Kanoria, “Modeling and analysis of vibration of a gold nanobeam under two temperatures theory,” J. Eng. Solid Mech., vol. 5, no. 1, pp. 15–30, 2017. DOI: 10.5267/j.esm.2016.10.003.
   Google Scholar
• S. Mondal, P. Pal, and M. Kanoria, “Transient response in a thermoelastic half-space solid due to a laser pulse under three theories with memory-dependent derivative,” Acta Mech., vol. 230, no. 1, pp. 179–199, 2019. DOI: 10.1007/s00707-018-2307-z.
   Web of Science ®Google Scholar
• S. Mondal, S. H. Mallik, and M. Kanoria, “Fractional order two temperatures dual-phaselag thermoelasticity with variable thermal conductivity,” Int. Sch. Res. Notices, vol. 2014, pp. 646049, 2014. DOI: 10.1155/2014/646049.
   PubMedGoogle Scholar
• P. Chadwick and I. N. Sneddon, “Plane waves in an elastic solid conducting heat,” J. Mech. Phys. Solids, vol. 6, no. 3, pp. 223–230, 1958. DOI: 10.1016/0022-5096(58)90027-9.
   Web of Science ®Google Scholar
• G. Paria, “On magneto-thermo-elastic plane waves,” Math. Proc. Camb. Phil. Soc., vol. 58, no. 3, pp. 527–531, 1962. DOI: 10.1017/S030500410003680X.
   Web of Science ®Google Scholar
• A. H. Nayfeh and S. Nemat-Nasser, “Thermoelastic waves in solids with thermal relaxation,” Acta Mech., vol. 12, no. 1–2, pp. 53–59, 1971. DOI: 10.1007/BF01178389.
   Web of Science ®Google Scholar
• A. H. Nayfeh and S. Nemat-Nasser, “Electromagneto-thermoelastic plane waves in solids with thermal relaxation,” J. Appl. Mech., vol. 39, no. 1, pp. 108–113, 1972. DOI: 10.1115/1.3422596.
   Web of Science ®Google Scholar
• P. Puri, “Plane waves in generalized thermoelasticity,” Int. J. Eng. Sci., vol. 11, no. 7, pp. 735–744, 1973. DOI: 10.1016/0020-7225(73)90003-7.
   Web of Science ®Google Scholar
• V. K. Agarwal, “On electromagneto-thermoelastic plane waves,” Acta Mech., vol. 34, no. 3–4, pp. 181–191, 1979. DOI: 10.1007/BF01227983.
   Web of Science ®Google Scholar
• S. K. Roychoudhuri, “Effects of rotation and relaxation times on plane waves in generalized thermoelasticity,” J. Elast., vol. 15, pp. 59–68, 1985. DOI: 10.1007/BF00041305.
   Web of Science ®Google Scholar
• S. B. Sinha and K. A. Elsibai, “Reflection of thermoelastic waves at a solid half-space with two relaxation times,” J. Therm. Stresses, vol. 19, no. 8, pp. 749–777, 1996. DOI: 10.1080/01495739608946205.
   Web of Science ®Google Scholar
• J. N. Sharma, V. Kumar, and D. Chand, “Reflection of generalized thermoelastic waves from the boundary of a half space,” J. Therm. Stresses, vol. 26, no. 10, pp. 925–942, 2003. DOI: 10.1080/01495730306342.
   Web of Science ®Google Scholar
• S. K. Roy Choudhuri and M. Banerjee, “Magneto-viscoelastic plane waves in rotating media in the generalized thermoelasticity II,” Int. J. Math. Math. Sciences, vol. 2005, no. 11, pp. 1819–1834, 2005. DOI: 10.1155/IJMMS.2005.1819.
   Google Scholar
• M. I. A. Othman and Y. Q. Song, “Reflection of magneto-thermoelastic waves with two relaxation times and temperature dependent elastic moduli,” Appl. Math. Model., vol. 32, no. 4, pp. 483–500, 2008. DOI: 10.1016/j.apm.2007.01.001.
   Web of Science ®Google Scholar
• N. D. Gupta, A. Lahiri, and N. C. Das, “Reflection of coupled generalized temperature rate dependent thermoelastic waves on a half space,” Math. Mech. Solids, vol. 17, no. 6, pp. 543–556, 2012. DOI: 10.1177/1081286511426914.
   Web of Science ®Google Scholar
• B. Sing, “Wave Propagation in a Green–Naghdi Thermoelastic Solid with Diffusion,” Int. J. Thermophy., vol. 34, no. 3, pp. 553–566, 2013. DOI: 10.1007/s10765-013-1444-9.
   Web of Science ®Google Scholar
• M. N. M. Allam, S. Z. Rida, S. M. Abo-Dahab, R. A. Mohamed, and A. A. Kilany, “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. Therm. Stresses, vol. 37, no. 4, pp. 471–487, 2014. DOI: 10.1080/01495739.2013.870861.
   Web of Science ®Google Scholar
• A. M. Abd-Alla, M. I. A. Othman, and S. M. Abo-Dahab, “Reflection of plane waves from electro-magneto-thermoelastic half-space with a dual-phase-lag model,” Comp. Mat. Continua, vol. 51, pp. 63–79, 2016.
   Web of Science ®Google Scholar
• M. I. A. Othman, S. M. Abo-Dahab, and N. S. O. Alsebaey, “Reflection of plane waves from a rotating magneto-thermoelastic medium with two temperatures and initial stress under three theories,” Mech. Mech. Eng., vol. 21, pp. 217–232, 2017.
   Google Scholar
• S. Biswas and N. Sarkar, “Fundamental solution of the steady oscillations equations in porous thermoelastic medium with dual-phase-lag model,” Mech. Mat., vol. 126, pp. 140–147, 2018. DOI: 10.1016/j.mechmat.2018.08.008.
   Web of Science ®Google Scholar
• Y. Li, W. Wang, P. Wei, and C. Wang, “Reflection and transmission of elastic waves at an interface with consideration of couple stress and thermal wave effects,” Meccanica, vol. 53, no. 11–12, pp. 2921–2938, 2018. 2018. DOI: 10.1007/s11012-018-0842-2.
   Web of Science ®Google Scholar
• S. M. Abo-Dahab, “Reflection of generalized magneto-thermoelastic waves with two temperatures under influence of thermal shock and initial stress,” J. Heat Transfer, vol. 140, no. 10, pp. 102005-1–102005-8, 2018. DOI: 10.1115/1.4040258.
   Web of Science ®Google Scholar
• Sudip Mondal and Sadek Hossain Mallik and M. Kanoria, “Fractional order two-temperature dual-phase-lag thermoelasticity with variable thermal conductivity,” International Scholarly Research Notices, vol 2014, pp. 1–13, 2014. DOI: 10.1155/2014/646049.
   Google Scholar
• N. Sarkar and S. K. Tomar, “Plane waves in nonlocal thermoelasticsolid with voids,” J. Therm. Stresses, vol. 42, no. 5, pp. 580–606, 2019. DOI: 10.1080/01495739.2018.1554395.
   Web of Science ®Google Scholar
• J. Ignaczak and M. Ostoja-Starzewski, 2010, Thermoelasticity with finite wave speeds. Oxford University Press, Oxford.
   Google Scholar
• D. S. Chandrasekharaiah, “Thermoelastic plane waves without energy dissipation,” Mechanics Res. Commun., vol. 23, no. 5, pp. 549–555, 1996. DOI: 10.1016/0093-6413(96)00056-0.
   Web of Science ®Google Scholar
• J. N. Sharma, D. Grover, and D. Kaur, “Mathematical modelling and analysis of bulk waves in rotating generalized thermoelastic media with voids,” Appl. Math. Model., vol. 35, no. 7, pp. 3396–3407, 2011. DOI: 10.1016/j.apm.2011.01.014.
   Web of Science ®Google Scholar
• J. D. Achenbach, 1976, Wave propagation in elastic solids. New York: North-Holland.
   Google Scholar
• Y. Li, P. Wei, and C. Wang, “Propagation of thermoelastic waves across an interface with consideration of couple stress and second sound,” Math. Mech. Solids, vol. 24, no. 1, pp. 235–257, 2019. DOI: 10.1177/1081286517736999.
   Web of Science ®Google Scholar
• Y. Li, L. Li, P. Wei, and C. Wang, “Reflection and refraction of thermoelastic waves at an interface of two couple-stress solids based on Lord-Shulman thermoelastic theory,” Appl. Math. Model., vol. 55, pp. 536–550, 2018. DOI: 10.1016/j.apm.2017.10.040.
   Web of Science ®Google Scholar
• Y. Li and P. Wei, “Reflection and transmission of thermo-elastic waves without energy dissipation at the interface of two dipolar gradient elastic solids,” J. Acoust. Soc. Am., vol. 143, no. 1, pp. 550–562, 2018. DOI: 10.1121/1.5020780.
   PubMed Web of Science ®Google Scholar