Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Wave propagation at free surface in thermoelastic medium under modified Green-Lindsay model with non-local and two temperature

  • Sachin Kaushal (Department of Mathematics, School of Chemical Engineering and Physical Sciences, Lovely Professional University-Phagwara) ;
  • Rajneesh Kumar (Department of Mathematics, Kurukshetra University Kurukshetra) ;
  • Indu Bala (Department of Mathematics, School of Chemical Engineering and Physical Sciences, Lovely Professional University-Phagwara) ;
  • Gulshan Sharma (Department of Mathematics, School of Chemical Engineering and Physical Sciences, Lovely Professional University-Phagwara)
  • Received : 2023.02.21
  • Accepted : 2024.04.01
  • Published : 2024.04.25
⟨ Previous Next ⟩

Abstract

The present paper is focused on the study of the propagation of plane waves in thermoelastic media under a modified Green-Lindsay (MG-L) model having the influence of non-local and two temperature. The problem is formulated for the considered model in dimensionless form and is explained by using the reflection phenomenon. The plane wave solution of these equations indicates the existence of three waves namely Longitudinal waves (LD-Wave), Thermal waves (T-wave), and Shear waves (SV-wave) from a stress-free surface. The variation of amplitude ratios is computed analytically and depicted graphically against the angle of incidence to elaborate the impact of non-local, two temperature, and different theories of thermoelasticity. Some particular cases of interest are also deduced from the present investigation. The present study finds applications in a wide range of problems in engineering and sciences, control theory, vibration mechanics, and continuum mechanics.

Keywords

References

  1. Abo-Dahab, S.M. and Lofty, Kh. (2017), "Two-temperature plane strain problem in a semiconducting medium under photothermal theory", Wave. Random Complex Media, 27(1), 67-91. https://doi.org/10.1080/17455030.2016.1203080.
  2. Bajpai, A. and Sharma, P.K. (2021), "Impact of two temperatures on a generalized thermoelastic plate with thermal loading", Appl. Anal., Comput. Math. Model. Eng., 897, 69-81. https://doi.org/10.1007/978-981-19-1824-7_5.
  3. Chen, P.J. and Gurtin, M.E. (1968), "On a theory of heat conduction involving two temperatures", Zeitschrift f Angew. Math. Phys. (Z.A.M.P), 19(4), 614-627.
  4. Dhaliwal, R.S. and Singh, A. (1980), Dynamic Coupled Thermoelasticity, Hindustan Publication Corporation, New Delhi, India.
  5. El-Bary, A.A. (2021), "Hyperbolic two-temperature generalized thermoelasticity with fractional order strain of solid cylinder", J. Eng. Therm. Sci., 1(2), 30-42. https://doi.org/10.21595/jets.2021.21969.
  6. Eringen, A.C. and Edelen, D.G.B. (1972), "On nonlocal elasticity", Int. J. Eng. Sci., 10(3), 233-248. https://doi.org/10.1016/0020-7225(72)90039-0.
  7. Ezzat, M.A., El-Karamany, A.S. and El-Bary, A.A. (2015), "On thermo-viscoelasticity with variable thermal conductivity and fractional-order heat transfer", Int. J. Thermophys., 36(7), 1684-1697. https://doi.org/10.1007/s10765-015-1873-8.
  8. Ezzat, M.A., El-Karamany, A.S., El-Bary, A.A. and Fayik, M.A. (2013), "Fractional calculus in one-dimensional isotropic thermo-viscoelasticity", C.R. Mecanique, 341(7), 553-566. https://doi.org/10.1016/j.crme.2013.04.001.
  9. Fernaindez, J.R. and Quintanilla, R. (2021), "Two-temperatures thermo-porous-elasticity with microtemperatures", Appl. Math. Lett., 111, 106628. https://doi.org/10.1016/j.aml.2020.106628.
  10. Green, A.E. and Lindsay, K.A. (1972), "Thermoelasticity", J. Elast., 2, 1-7. https://doi.org/10.1007/BF00045689.
  11. Kaushal, S., Kumar, R. and Miglani, A. (2010), "Response of frequency domain in generalized thermoelasticity with two temperatures", Int. J. Eng. Phys. Thermophys., 83(5), 1080-1088. https://doi.org/10.1007/s10891-010-0433-0.
  12. Kaushal, S., Kumar, R. and Miglani, A. (2011), "Wave propagation in temperatures rate dependent thermoelasticity with two temperatures", Math. Sci., 5,125-146.
  13. Kumar, R., Ghangas, S. and Vashishth, A.K. (2021), "Fundamental and plane wave solutions in non-local bio-thermoelasticity diffusion theory", Couple. Syst. Mech., 10(1), 21-38. https://doi.org/10.12989/csm.2021.10.1.021.
  14. Kumar, R., Kaushal, S. and Sharma, G. (2022), "Mathematical model for the deformation in a modified Green-Lindsay thermoelastic medium with nonlocal and two-temperature effects", J. Appl. Mech. Tech. Phys., 63, 448-457. https://doi.org/10.1134/S0021894422030099.
  15. Kumar, R., Kaushal, S., Reen, L.S. and Garg, S.K. (2016), "Deformation due to various sources in transversely isotropic thermoelastic material without energy dissipation and with two-temperature", Mater. Phys. Mech., 27(1), 22-31.
  16. Lazar, M. and Agiasofitou, E. (2011), "Screw dislocation in nonlocal anisotropic elasticity", Int. J. Eng. Sci., 49(12), 1404-1414. https://doi.org/10.1016/j.ijengsci.2011.02.011.
  17. Lord, H.W. and Shulman, Y. (1967), "A generalized dynamical theory of thermoelasticity", J. Mech. Phys. Solid., 15(5), 299-309. https://doi.org/10.1016/0022-5096(67)90024-5.
  18. Luo, P., Li, X. and Tian, X. (2021), "Nonlocal thermoelasticity and its application in thermoelastic problem with temperature-dependent thermal conductivity", Eur. J. Mech.-A/Solid., 87, 104204. https://doi.org/10.1016/j.euromechsol.2020.104204.
  19. Mahdy, A.M.S., Lotfy, Kh., El-Bary, A.A. and Sarhan, H.H. (2021), "Effect of rotation and magnetic field on a numerical-refined heat conduction in a semiconductor medium during photo-excitation processes", Eur. Phys. J. Plus, 136, 553. https://doi.org/10.1140/epjp/s13360-021-01552-3.
  20. Mahdy, A.M.S., Lotfy, Kh., El-Bary, A.A. and Tayel, I.M. (2021), "Variable thermal conductivity and hyperbolic two-temperature theory during magneto-photothermal theory of semiconductor induced by laser pulses", Eur. Phys. J. Plus, 136, 1-21. https://doi.org/10.1140/epjp/s13360-021-01633-3.
  21. Quintanilla, R. (2018), "Some qualitative results for a modification of the Green-Lindsay thermoelasticity", Meccanica, 53(14), 3607-3613. https://doi.org/10.1007/s11012-018-0889-0.
  22. Sarkar, N. and De, S. (2020), "Waves in magneto-thermoelastic solids under modified Green-Lindsay model", J. Therm. Stress., 43(5), 594-611. https://doi.org/10.1080/01495739.2020.1712286.
  23. Shakeriaski, F., Ghodrat, M., Diaz, J.E. and Behnia, M. (2020), "Modified Green-Lindsay thermoelasticity wave propagation in elastic materials under thermal shocks", J. Comput. Des. Eng., 8(1), 36-54. https://doi.org/10.1093/jcde/qwaa061.
  24. Sharma, S. and Khator, S. (2021), "Power generation planning with reserve dispatch and weather uncertainties including penetration of renewable sources", Int. J. Smart Grid Clean Energy, 10(4), 292-303. https://doi.org/10.12720/sgce.10.4.292-303.
  25. Sharma, S. and Khator, S. (2022), "Micro-Grid planning with aggregator's role in the renewable inclusive prosumer market", J. Power Energy Eng., 10(4), 47-62. https://doi.org/10.4236/jpee.2022.104004.
  26. Yasein, M., Mabrouk, N., Lotfy, Kh. and EL-Bary, A.A. (2019), "The influence of variable thermal conductivity of semiconductor elastic medium during photothermal excitation subjected to thermal ramp type", Result. Phys., 25(12), 4731-4740. https://doi.org/10.1016/j.rinp.2019.102766.
  27. Youssef, H.M. (2006), "Theory of two-temperature-generalized thermoelasticity", MA J. Appl. Math., 71(3), 383-390. https://doi.org/10.1093/imamat/hxh101.
  28. Yu, Y.J., Xue, Z. and Tian, X. (2018), "A modified Green-Lindsay thermoelasticity with strain rate to eliminate the discontinuity", Meccanica, 53, 2543-2554. https://doi.org/10.1007/s11012-018-0843-1.