DOI QR코드

DOI QR Code

Influence of gravity, locality, and rotation on thermoelastic half-space via dual model

  • Samia M. Said (Department of Mathematics, Faculty of Science, Zagazig University)
  • Received : 2023.12.22
  • Accepted : 2024.02.05
  • Published : 2024.02.25

Abstract

In this paper, Eringen's nonlocal thermoelasticity is constructed to study wave propagation in a rotating two-temperature thermoelastic half-space. The problem is applied in the context of the dual-phase-lag (Dual) model, coupled theory (CD), and Lord-Shulman (L-S) theory. Using suitable non-dimensional fields, the harmonic wave analysis is used to solve the problem. Comparisons are carried with the numerical values predicted in the absence and presence of the gravity field, a nonlocal parameter as well as rotation. The present study is valuable for the analysis of nonlocal thermoelastic problems under the influence of the gravity field, mechanical force, and rotation.

Keywords

References

  1. Abbas, I., Hobiny, A. and Marin, M. (2020), "Photo-thermal interactions in a semi-conductor material with cylindrical cavities and variable thermal conductivity", J. Taibah Univ. Sci., 14(1), 1369-1376. https://doi.org/10.1080/16583655.2020.1824465.
  2. Abbas, I., Hobiny, A., Vlase, S. and Marin, M. (2022), "Generalized thermoelastic interaction in a half-space under a nonlocal thermoelastic model", Math., 10(13), 2168. https://doi.org/10.3390/math10132168.
  3. Abbas, I.A. and Zenkour, A.M. (2014), "Dual-phase-lag model on thermoelastic interactions in a semi-infinite medium subjected to a ramp-type heating", J. Comput. Theor. Nanosci., 11(3), 642-645. http://doi.org/10.1166/jctn.2014.3407.
  4. Acharya, D.P. and Mondal, A. (2002), "Propagation of Rayleigh surface waves with small wavelengths in nonlocal visco-elastic solids", Sadhana, 27(12), 605-612. https://doi.org/10.1007/BF02703353.
  5. Alharbi, A.M., Said, S.M., Abd-Elaziz, E.M. and Othman, M.I.A. (2022), "Fiber-reinforced micropolar thermoelastic rotating solid with voids and two-temperature in the context of memory-dependent derivative", Geomech. Eng., 28(4), 347-358. https://doi.org/10.12989/gae.2022.28.4.347.
  6. Biot, M.A. (1956), "Thermoelasticity and irreversible thermodynamics", J. Appl. Phys., 27, 240-253. https://doi.org/10.1063/1.1722351.
  7. Biswas, S. (2020), "Fundamental solution of steady oscillations equations in nonlocal thermoelastic medium with voids", J. Therm. Stress., 43(3), 284-304. https://doi.org/10.1080/01495739.2019.1699482.
  8. Caputo, M. and Mainardi, F. (1971a), "A new dissipation model based on memory mechanism", Pure Appl. Geophys., 91(12), 134-147. https://doi.org/10.1007/BF00879562.
  9. Caputo, M. and Mainardi, F. (1971b), "Linear models of dissipation in anelastic solids", Rivista del Nuovo Cimento (Ser. II), 1(4), 161-198. https://doi.org/10.1007/BF02820620.
  10. Eringen, A.C. (1972a), "Nonlocal polar elastic continua", Int. J. Eng. Sci., 10(1), 1-16. https://doi.org/10.1016/0020-7225(72)90070-5.
  11. Eringen, A.C. (1974), "Theory of nonlocal thermoelasticity", Int. J. Eng. Sci., 12(12), 1063-1077. https://doi.org/10.1016/0020-7225(74)90033-0.
  12. Eringen, A.C. (2002), Nonlocal Continuum Field Theories, Springer, New York.
  13. Eringen, A.C. and Edelen, D.G.B. (1972b), "On nonlocal elastic", Int. J. Eng. Sci., 10 (3), 233-248. https://doi.org/10.1016/0020-7225(72)90039-0.
  14. Green, A.E. and Lindsay, K.A. (1972), "Thermoelasticity", J. Elasticity, 2(3), 1-7. https://doi.org/10.1007/BF00045689.
  15. Hobiny, A., Abbas, I., Alshehri, H. and Marin, M. (2022), "Analytical solutions of nonlocal thermoelastic Interaction on semi-infinite mediums induced by ramp-type heating", Symmetry, 14(5), 864. https://doi.org/10.3390/sym14050864.
  16. Kaliski, S., Rymarz, Cz. and Sobczyk, K. (1992), "Surface waves in nonlocal media and in media with a microstructure", Stud. Appl. Mech.-B: Wave., 30, 261-270. https://doi.org/10.1016/B978-0-444-98690-0.50031-6
  17. Karami, B., Janghorban, M. and Tounsi, A. (2018), "Nonlocal strain gradient 3D elasticity theory for anisotropic spherical nanoparticles", Steel Compos. Struct., 27(2), 201-216. https://doi.org/10.12989/scs.2018.27.2.201.
  18. Khurana, A. and Tomar, S.K. (2017), "Rayleigh-type waves in nonlocal micropolar solid half-space", Ultrasonic., 75, 162-168. https://doi.org/10.1016/j.ultras.2016.09.005.
  19. Lata, P. and Singh, S. (2019), "Effect of nonlocal parameter on nonlocal thermoelastic solid due to inclined load", Steel Compos. Struct., 33(1), 123-131. https://doi.org/10.12989/scs.2019.33.1.123.
  20. Lata, P., Kaur, I. and Singh, K. (2020), "Transversely isotropic thin circular plate with multi-dual-phase lag heat transfer", Steel Compos. Struct., 35(3), 343-351. http://doi.org/10.12989/scs.2020.35.3.343.
  21. Lord, H.W. and Shulman, Y.A. (1967), "Generalized dynamical theory of thermoelasticity", J. Mech. Phys. Solid., 15(5), 299-309. https://doi.org/10.1016/0022-5096(67)90024-5.
  22. Marin, M., Hobiny, A. and Abbas, I. (2021), "The effects of fractional time derivatives in poro-thermoelastic materials using finite element method", Math., 9(14), Art. No. 1606. https://doi.org/10.3390/math9141606.
  23. Marin, M., Seadawy, A., Vlase, S. and Chirila, A. (2022), "On mixed problem in thermoelasticity of type III for Cosserat media", J. Taibah Univ. Sci., 16(1), 1264-1274. https://doi.org/10.1080/16583655.2022.2160290.
  24. Othman, M.I.A., Fekry, M. and Marin, M. (2020), "Plane waves in generalized magneto-thermo-viscoelastic medium with voids under the effect of initial stress and laser pulse heating", Struct. Eng. Mech., 73(6), 621-629. https://doi.org/10.12989/sem.2020.73.6.621.
  25. Othman, M.I.A., Zidan, M.E.M. and Mohamed, I.E.A. (2021), "Dual-phase-lag model on thermo-microstretch elastic solid under the effect of initial stress and temperature-dependent", Steel Compos. Struct., 38(4), 355-363. https://doi.org/10.12989/scs.2021.38.4.355.
  26. Ozisik, M.N. and Tzou, D.Y. (1994), "On the wave theory in heat conduction", J. Heat Transf., 116(3), 526-535. https://doi.org/10.1115/1.2910903.
  27. RoyChoudhuri, S.K. (2007), "One-dimensional thermoelastic waves in elastic half-space with dual phase lag effects", J. Mech. Mater. Struct., 2(3), 489-503. https://doi.org/10.2140/jomms.2007.2.489.
  28. Roy, I., Acharya, D.P. and Acharya, S. (2015), "Rayleigh wave in a rotating nonlocal magneto-elastic half-plane", J. Theor. Appl. Mech., 45(4), 61-78. https://doi.org/10.1515/jtam-2015-0024.
  29. Said, S.M. (2016), "Influence of gravity on generalized magneto-thermoelastic medium for three-phase-lag model", J. Comput. Appl. Math., 291, 142-157. http://doi.org/10.1016/j.cam.2014.12.016.
  30. Said, S.M. (2020), "Novel model of thermo-magneto-viscoelastic medium with variable thermal conductivity under effect of gravity", Appl. Math. Mech., 41(5), 819-832. https://doi.org/10.1007/s10483-020-2603-9.
  31. Said, S.M. (2022), "A viscoelastic-micropolar solid with voids and microtemperatures under the effect of the gravity field", Geomech. Eng., 31(2), 159-166. https://doi.org/10.12989/gae.2022.31.2.159.
  32. Said, S.M. (2023a), "A study on the frame of a memory-dependent derivative in a micropolar thermoelastic medium under the effect of the variable thermal conductivity", Mech. Bas. Des. Struct. Mach., 51(2), 665-681. https://doi.org/10.1080/15397734.2020.1851255.
  33. Said, S.M. (2023b), "A novel model of a nonlocal porous thermoelastic solid with temperature-dependent properties using an eigenvalue approach", Geomech. Eng., 32(2), 137-144. https://doi.org/10.12989/gae.2023.32.2.137
  34. Schoenberg, M. and Censor, D. (1973), "Elastic waves in rotating media", Quart. Appl. Math., 31(1), 115-125. https://doi.org/10.1090/qam/99708
  35. Singh, B. (2013), "Wave propagation in dual-phase-lag anisotropic thermoelasticity", Continuum Mech. Thermodyn., 25(9), 675-683. https://doi.org/10.1007/s00161-012-0261-x.
  36. Singh, B. (2021b), "Rayleigh-type surface waves in a nonlocal thermoelastic solid half space with voids", Wave. Random Complex Media, 31(6), 2103-2114. https://doi.org/10.1080/17455030.2020.1721612.
  37. Singh, B. and Bijarnia, R. (2021a), "Nonlocal effects on propagation of waves in a generalized thermoelastic solid half space", Struct. Eng. Mech., 77(4), 473-479. https://doi.org/10.12989/sem.2021.77.4.473.
  38. Singh, B., Sangwan, A. and Singh, J. (2022), "Nonlocal effects on Rayleigh-type surface wave in a micropolar piezoelectric medium", Vietnam J. Mech., 44(1), 1-13. https://doi.org/10.15625/0866-7136/16539.
  39. Sur, A. and Kanoria, M. (2018), "Thermoelastic interaction in a three-dimensional layered sandwich structure", Mech. Adv. Compos. Struct., 5, 187-198. http://doi.org/10.22075/MACS.2018.14201.1141.
  40. Tzou, D.Y. (1995a), "Experimental support for the lagging behavior in heat propagation", J. Thermophys. Heat Transf., 9(4), 686-693. https://doi.org/10.2514/3.725.
  41. Tzou, D.Y. (1995b), "A unified field approach for heat conduction from macro to micro-scales", ASME J. Heat Transf., 117(1), 8-16. https://doi.org/10.1115/1.2822329.
  42. Youssef, H.M. (2005a), "Theory of two-temperature generalized thermoelasticity", IMA J. Appl. Math., 71(3), 383-390. https://doi.org/10.1093/imamat/hxh101.
  43. Youssef, H.M. (2005b), "State-space approach on generalized thermoelasticity for an infinite material with a spherical cavity and variable thermal conductivity subjected to ramp type heating", Can. Appl. Math. Quart., 13(4), 369-390.