Coupled systems mechanics

  • 제10권2호
  • /
  • Pages.143-159
  • /
  • 2021
  • /
  • 2234-2184(pISSN)
  • /
  • 2234-2192(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Reflection of plane waves from the boundary of a thermo-magneto-electroelastic solid half space

  • Singh, Baljeet (Department of Mathematics, Post Graduate Government College) ;
  • Singh, Aarti (Department of Mathematics, Maharishi Markandeshwar University)
  • 투고 : 2020.11.28
  • 심사 : 2021.05.15
  • 발행 : 2021.04.25
⟨ 이전 논문 다음 논문 ⟩

초록

The theory of generalized thermo-magneto-electroelasticity is employed to obtain the plane wave solutions in an unbounded, homogeneous and transversely isotropic medium. Reflection phenomena of plane waves is considered at a stress free and thermally insulated surface. For incidence of a plane wave, the expressions of reflection coefficients and energy ratios for reflected waves are derived. To explore the characteristics of reflection coefficients and energy ratios, a quantitative example is set up. The half-space of the thermo-magneto-electroelastic medium is assumed to be made out of lithium niobate. The dependence of reflection coefficients and energy ratios on the angle of incidence is illustrated graphically for different values of electric, magnetic and thermal parameters.

키워드

참고문헌

  1. Abd-Alla, A.M. and Othman, M.I.A. (2016), "Reflection of plane waves from electro-magneto-thermoelastic half-space with a dual-phase-lag model", CMC, 51, 63-79.
  2. Abo-Dahab, S.M. and Singh, B. (2013), "Rotational and voids effect on the reflection of P waves from stress-free surface of an elastic half-space under magnetic field and initial stress without energy dissipation", Appl. Math. Model., 37, 8999-9011. https://doi.org/10.1016/j.apm.2013.04.033.
  3. Achenbach, J.D. (1973), "Wave propagation in elastic solids", A Volume in North-Holland Series in Applied Mathematics and Mechanics, North-Holland, Elsevier.
  4. Amendola, G. (2000), "On thermodynamic conditions for the stability of a thermoelectromagnetic system", Math. Meth. Appl. Sci., 23, 17-39. https://doi.org/10.1002/(SICI)1099-1476(20000110)23:1<17::AID-MMA101>3.0.CO;2-%23.
  5. Aouadi, M. (2007), "The generalized theory of thermo-magnetoelectroelasticity", Technische Mechanik, 27, 133-146.
  6. Baksi, A. and Bera, R.K. (2005), "Eigen function method for the solution of magneto-thermoelastic problems with thermal relaxation and heat source in three dimension", Math. Comput. Model., 42, 533-552. https://doi.org/10.1016/j.mcm.2005.01.032.
  7. Coleman, B.D. and Dill, E.H. (1971), "Thermodynamic restrictions on the constitutive equations of electromagnetic theory", Z. Angew. Math. Phys., 22, 691-702. https://doi.org/10.1007/BF01587765.
  8. Dai, H.L. and Rao, Y.N. (2011), "Investigation on electro-magneto-thermo-elastic interaction of functionally graded piezoelectric hollow spheres", Struct. Eng. Mech., 40(1), 49-64. http://doi.org/10.12989/sem.2011.40.1.049.
  9. Das, N.C., Lahiri, A., Sarkar, S. and Basu, S. (2008), "Reflection of generalized thermoelastic waves from isothermal and insulated boundaries of a half space", Comput. Math. Appl., 56, 2795-2805. https://doi.org/10.1016/j.camwa.2008.05.042.
  10. Das, P. and Kanoria, M. (2009), "Magneto-thermo-elastic waves in an infinite perfectly conducting elastic solid with energy dissipation", Appl. Math. Mech., 30, 221-228. https://doi.org/10.1007/s10483-009-0209-6.
  11. Dhaliwal, R.S. and Sherief. H.H. (1980), "Generalized thermoelasticity for anisotropic media", Quart. Appl. Math., 33, 1-8. https://doi.org/10.1090/qam/575828.
  12. Dorfmann, L. and Ogden, R.W. (2014), Nonlinear Theory of Electroelastic and Magnetoelastic Interactions, New York, Springer.
  13. Ezzat, M.A. (1997), "State space approach to generalized magneto-thermoelasticity with two relaxation times in a medium of perfect conductivity", Int. J. Eng. Sci., 35, 741-752. https://doi.org/10.1016/S0020-7225(96)00112-7.
  14. Hsieh, R.K.T. (1990), "Mechanical modelling of new electromagnetic materials", Proc. IUTAM Symposium, Stockholm, Sweden, April.
  15. Kaliski, S. (1985), "Wave equations of thermo-electro-magneto-elasticity", Proc. Vib. Prob., 6, 231-263.
  16. Kondaiah, P., Shankar, K. and Ganesan, N. (2013), "Pyroelectric and pyromagnetic effects on behavior of magnetoelectro-elastic plate", Coupl. Syst. Mech., 2(1), 1-22. http://doi.org/10.12989/csm.2013.2.1.001.
  17. Lata, P. and Kaur, I. (2019), "Thermomechanical interactions in a transversely isotropic magneto thermoelastic solids with two temperatures and rotation due to time harmonic sources", Coupl. Syst. Mech., 8(3), 219-224. http://doi.org/10.12989/csm.2019.8.3.219.
  18. Li, J.Y. (2003), "Uniqueness and reciprocity theorems for linear thermo-electro-magnetoelasticity", Q. J. Mech. Appl. Math., 56, 35-43. http://doi.org/10.1093/qjmam/56.1.35.
  19. Lord, H. and Shulman, Y. (1967), "A generalized dynamical theory of thermoelasticity", J. Mech. Phys. Solid., 15, 299-309. https://doi.org/10.1016/0022-5096(67)90024-5.
  20. Moreno-Navarro, P., Ibrahimbegovich, A. and Perez-Aparicio, J.L. (2018), "Linear elastic mechanical system interacting with coupled thermo-electro-magnetic fields", Coupl. Syst. Mech., 7, 5-25. http://doi.org/10.12989/csm.2018.7.1.005.
  21. Nayfeh, A.H. and Nemat-Nasser, A. (1971), "Thermoelastic waves in solids with thermal relaxation", Acta Mechanica, 12, 53-64. https://doi.org/10.1007/BF01178389.
  22. Nayfeh, A.H. and Nemat-Nasser, A. (1972), "Electro-magneto-thermoelastic plane waves in solids with thermal relaxation", J. Appl. Mech., 39, 108-113. https://doi.org/10.1115/1.3422596.
  23. Ogden, R.W. and Steigmann, D.J. (2011), "Mechanics and electrodynamics of magneto- and electro-elastic materials", CISM Courses and Lctures, Vol. 527, Springer-Verlag.
  24. Paria, G. (1962), "On Magneto-thermo-elastic plane waves", Math. Proc. Camb. Phil. Soc., 58, 527-531. https://doi.org/10.1017/S030500410003680X.
  25. Ponnusamy, P. and Selvamani, R. (2012), "Dispersion analysis of generalized magneto-thermoelastic waves in a transversely isotropic cylindrical panel", J. Therm. Stress., 35, 1119-1142. https://doi.org/10.1080/01495739.2012.720496.
  26. Roychoudhuri, S.K. and Chatterjee, G. (1990), "A coupled magneto-thermoelastic problem in a perfectly conducting elastic half-space with thermal relaxation", Int. J. Math Mech. Sci., 13, 567-578. https://doi.org/10.1155/S0161171290000801.
  27. Sarkar, N., De, S. and Sarkar, N. (2019), "Memory response in plane wave reflection in generalized magnetothermoelasticity", J. Electromagnet. Waves Appl., 33, 1354-1374. ps://doi.org/10.1080/09205071.2019.1608318.
  28. Sarkar, N. and De, S. (2020), "Waves in magneto-thermoelastic solids under modified Green-Lindsay model", J. Therm. Stress., 43, 594-611. https://doi.org/10.1080/01495739.2020.1712286.
  29. Sharma, J.N., Kumar, V. and Chand, D. (2003), "Reflection of generalized thermoelastic waves from the boundary of a half-space", J. Therm. Stress., 26, 925-942. https://doi.org/10.1080/01495730306342.
  30. Sherief, H.H. and Youssef H.M. (2004), "Short time solution for a problem in magneto-thermoelasticity with thermal relaxation", J. Therm. Stress., 27, 537-559. https://doi.org/10.1080/01495730490451468.
  31. Singh, B., Singh, A. and Sharma, N. (2016), "Propagation of plane waves in a generalized thermo-magneto-electro-elastic medium", Tech. Mech., 36, 199-212. https://doi.org/10.24352/UB.OVGU-2017-006.
  32. Singh, B. (2020), "Wave propagation in two-temperature porothermoelasticity", Int. J. Thermophys., 41, https://doi.org/10.1007/s10765-020-02670-3.
  33. Tiwari, R. and Mukhopadhyay, S. (2017), "On electromagneto-thermoelastic plane waves under Green-Naghdi theory of thermoelasticity-II", J. Therm. Stress., 40, 1040-1062. https://doi.org/10.1080/01495739.2017.1307094.
  34. Vinyas, M. and Kattimani, S.C. (2017), "Multiphysics response of magneto-electro-elastic beams in thermo-mechanical environment", Coupl. Syst. Mech., 6(3), 351-367. http://doi.org/10.12989/csm.2017.6.3.351.
  35. Weis, R.S. and Gaylord, T.K. (1985), "Summary of physical properties and crystal structure", Appl. Phys. A., 37, 191-203. https://doi.org/10.1007/BF00614817
  36. Yakhno, V.G. (2018), "An explicit formula for modeling wave propagation in magneto-electro-elastic materials", J. Electromagnet. Wave. Appl., 32, 899-912. https://doi.org/10.1080/09205071.2017.1410076
  37. Zhang, R. (2013), "Reflection and refraction of plane waves at the interface between magneto-electroelastic and liquid media", Theor. Appl. Mech., 40, 427-439. https://doi.org/10.2298/TAM1303427Z.
  38. Zhang, R., Pang, Y. and Feng, W. (2014), "Propagation of Rayleigh waves in a magneto-electro-elastic half-space with initial stress", Mech. Adv. Mater. Struct., 21, 538-543. https://doi.org/10.1080/15376494.2012.699595.