Coupled systems mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Modeling memory-dependent derivative on photothermoelastic half space in the presence of non-local and hyperbolic two temperatures

  • Rajneesh Kumar (Department of Mathematics, Kurukshetra University) ;
  • Nidh Sharma (Department of Mathematics, Maharishi Markandeshwar University Mullana) ;
  • Supriya Chopra (Department of Mathematics, Government College for Women)
  • Received : 2024.07.12
  • Accepted : 2025.04.09
  • Published : 2025.04.25
⟨ Previous Next ⟩

Abstract

The purpose of this paper is developed a new model of photothermoelastic with memory-dependent derivatives (PMDD) under non-local (NL) parameter, dual phase lag (DPL) and hyperbolic two temperature (HTT). The governing coupled equations of the considered model with time delay and kernel function, which can be chosen freely according to the necessity of applications, are applied to a two-dimensional problem of a half-space. Integral transform involving Laplace and Fourier transforms reduced the governing equations into ordinary differential equation. The arbitrary constants in the solution are determined by considering the loading environment on the surface. Three different categories of the sources are taken to explore the application as (i) normal force (ii) thermal source (iii) carrier density source. In the new domain, the closed form expressions of physical quantities like displacement, normal stress, conductive temperature field and carrier density distribution are derived. The numerical inversion method is employed to recover the results in a physical domain. The impact of non-local parameter, dual phase lag and hyperbolic two-temperature with and without MDD (memory dependent derivative) along with variations of all kernel functions on physical field variables are presented in form of graphs. Unique cases are also explored. The problem assumes great significance in an earthquake region when we think of variation of particle motion as a possible precursor for earthquake prediction. The results obtained are also helpful in designing the semiconductor materials in the course of coupled elastic, thermal, plasma waves and also find the application in the material and engineering sciences.

Keywords

References

  1. Abo Dahab, S.M., Lotfy, Kh. and Gohaly, A. (2015), "Rotation and magnetic field effect on surface waves propagation in an elastic layer lying over a generalized thermoelastic diffusive half-space with imperfect boundary", Math. Prob. Eng., 2015(1), 671783. https://doi.org/10.1155/2015/671783.
  2. Abo-Dahab, S. and Lotfy, Kh. (2015), "Generalized magneto-thermoelasticity with fractional derivative heat transfer for a rotation of a fibre-reinforced thermoelastic", J. Comput. Theor. Nanosci., 12(8), 1869-1881. https://doi.org/10.1166/jctn.2015.3972.
  3. Abouelregal, A., Marin, M. and Ö chsner, A. (2023), "The influence of a non-local Moore-GibsonThompson heat transfer model on an underlying thermoelastic material under the model of memorydependent derivatives", Contin. Mech. Thermodyn., 35(2), 545-562. https://doi.org/10.1007/s00161-023-01195-y.
  4. Abouelregal, A.E. and Dargail, H.E. (2021), "Memory and dynamic response of a thermoelastic functionally graded nanobeams due to a periodic heat flux", Mech. Bas. Des. Struct. Mach., 51(4), 2154-2176. https://doi.org/10.1080/15397734.2021.1890616.
  5. Abouelregal, A.E., Atta, D. and Sedighi, H.M. (2023), "Vibrational behavior of thermoelastic rotating nanobeams with variable thermal properties based on memory-dependent derivative of heat conduction model", Arch. Appl. Mech., 93, 197-220. https://doi.org/10.1007/s00419-022-02110-8.
  6. Abouelregal, A.E., Civalek, Ö . and Akgöz, B. (2025), "A size-dependent non-fourier heat conduction model for magneto-thermoelastic vibration response of nanosystems", J. Appl. Comput. Mech., 11(2), 344-357. https://doi.org/10.22055/jacm.2024.46746.4584.
  7. Abouelregal, A.E., Marin, M., Askar, S.S. and Foul, A. (2024), "Transient thermoelastic response in a semiinfinite medium subjected to a moving heat source: An implementation of the Moore-Gibson-Thompson model with higher-order memory-dependent derivatives", Mech. Time-depend. Mater., 28(3), 1555-1581. https://doi.org/10.1007/s11043-024-09672-w.
  8. Almond, D.P. and Patel, P.M. (1996), Photothermal Science and Techniques, Chapman and Hall, London. 
  9. Biot, M.A. (1956), "Thermoelasticity and irreversible thermodynamics", J. Appl. Phys., 27(3), 240-253. https://doi.org/10.1063/1.1722351.
  10. Caputo, M. (1967), "Linear models of dissipation whose Q is almost frequency independent—II", Geophys. J. Int., 13(5), 529-539. https://doi.org/10.1111/j.1365-246X.1967.tb02303.x.
  11. Diethelm, K. (2010), Analysis of Fractional Differential Equation: An Application- Oriented Exposition Using Differential Operators of Caputo Type, Springer, Berlin, Heideberg.
  12. Ezzat, M.A., El-Karamany, A.S. and El-Bary, A.A. (2014), "Generalized thermoviscoelasticity with memory dependent derivatives", Int. J. Mech. Sci., 89, 470-475. https://doi.org/10.1016/j.ijmecsci.2014.10.006.
  13. Ezzat, M.A., El-Karamany, A.S. and El-Bary, A.A. (2015), "A novel magneto thermoelasticity theory with memory dependent derivative", J. Electromagnet. Wave. Appl., 29(8), 1018-1031. https://doi.org/10.1080/09205071.2015.1027795.
  14. Ezzat, M.A., El-Karamany, A.S. and El-Bary, A.A. (2016), "Generalized thermoelasticity with memorydependent derivatives involving two-temperatures", Mech. Adv. Mater. Struct., 23, 545-553. https://doi.org/10.1080/15376494.2015.1007189.
  15. Green, A.E. and Naghdi, P.M. (1991), "A re-examination of the basic postulates of thermomechanics", Proc. Roy. Soc. London. Ser. A: Math. Phys. Sci., 432(1885), 171-194. https://doi.org/10.1098/rspa.1991.0012.
  16. Green, A.E. and Naghdi, P.M. (1992), "On undamped heat waves in an elastic solid", J. Therm. Stress., 15, 253-264. https://doi.org/10.1080/01495739208946136.
  17. Green, A.E. and Naghdi, P.M. (1993), "Thermoelasticity without energy dissipation", J. Elast., 31(3), 189-208. https://doi.org/10.1007/BF00044969.
  18. Hendy, M.H., El-Attar, S.I. and Ezzat, M.A. (2020), "On thermoelectric materials with memory- dependent derivative and subjected to a moving heat source", Microsyst. Technol., 26, 595-608. https://doi.org/10.1007/s00542-019-04519-8.
  19. Honig, G. and Hirdes, U. (1984), "A method for the numerical inversion of Laplace transforms", J. Comput. Appl. Math., 10(1), 113-132. https://doi.org/10.1016/0377-0427(84)90075-X.
  20. Jackson, W. and Amer, N.M. (1980), "Piezoelectric photoacoustic detection: Theory and experiment", J. Appl. Phys., 51(6), 3343-3353. https://doi.org/10.1063/1.328045.
  21. Jahangir, A., Tanvir, F. and Zenkour, A.M. (2020), "Reflection of photothermoelastic waves in a semiconductor material with different relaxations", Ind. J. Phys., 95, 51-59. https://doi.org/10.1007/s12648-020-01690-x.
  22. Kumar, R., Sharma, N. and Chopra, S. (2022), "Modelling of thermomechanical response in anisotropic photothermoelastic plate", Int. J. Mech. Eng., 7(6), 577-594.
  23. Kumar, R., Sharma, N. and Chopra, S. (2022), "Photothermoelastic interations under Moore- GibsonThompson thermoelasticity", Couple. Syst. Mech., 11(5), 459-483. https://doi.org/10.12989/csm.2022.11.5.459.
  24. 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.
  25. Lotfy, K. and Tantawi, R.S. (2020), "Photo-thermal-elastic interaction in a functionally graded material (FGM) and magnetic field", Silicon, 12, 295-303. https://doi.org/10.1007/s12633-019-00125-5.
  26. Lotfy, K., El-Bary, A.A. and Tantawi, R.S. (2019), "Effects of variable thermal conductivity of a small semiconductor cavity through the fractional order heat-magneto-photothermal theory", Eur. Phys. J. Plus, 134, 280. https://doi.org/10.1140/epjp/i2019-12631-1.
  27. Lotfy, Kh. (2012), "Mode-I crack in a two-dimensional fibre-reinforced generalized thermoelastic problem", Chin. Phys. B., 21, 014209. https://doi.org/10.1088/1674-1056/21/1/014209.
  28. Lotfy, Kh., Elidy, E. and Tantawi, R. (2021), "Piezo-photo-thermoelasticity transport process for hyperbolic two-temperature theory of semiconductor material", Int. J. Mod. Phys. C, 32(07), 2150088. https://doi.org/10.1142/S0129183121500881.
  29. Lotfy, Kh., Kumar, R., Hassan, W. and Gabr, M. (2018), "Thermomagnetic effect with microtemperature in a semiconducting photothermal excitation medium", Appl. Math. Mech., 39, 783-796. https://doi.org/10.1007/s10483-018-2339-9.
  30. Mahdy, A., Gepreel, Kh., Lotfy, Kh. and El-Bary, A. (2021), "A numerical method for solving the Rubella ailment disease model", Int. J. Mod. Phys. C, 32(07), 2150097. https://doi.org/10.1142/S0129183121500972.
  31. Mahdy, A., Mohamed, M.S., Lotfy, Kh., Alhazmi, M., El-Bary, A.A. and Raddadi, M.H. (2021), "Numerical solution and dynamical behaviors for solving fractional nonlinear Rubella ailment disease model", Result. Phys., 24(21), 2211-3797. https://doi.org/10.1016/j.rinp.2021.104091.
  32. Mandelis, A. (1987), Photoacoustic and Thermal wave Phenomena in Semiconductors, Elsevier Science, North-Holland, New York.
  33. Mandelis, A. and Michaelian, K.H. (1997), "Photoacoustic and photothermal science and engineering" Opt. Eng., 36(2), 301-302. https://doi.org/10.1117/1.601597
  34. McDonald, F.A. and Wetsel, G.C. (1978), "Generalized theory of the photoacoustic effect", J. Appl. Phys., 49(4), 2313-2322. https://doi.org/10.1063/1.325116.
  35. Nikolic, P.M. and Todorovic, D.M. (1989), "Photoacoustic and electroacoustic properties of semiconductors", Prog. Quantum. Electron., 13, 107-189. https://doi.org/10.1016/0079-6727(89)90006-2
  36. Sharma, K. (2010), "Boundary value problems in generalised thermodiffusive elastic medium", J. Solid Mech., 2(4), 348-362.
  37. Sharma, N. and Kumar, R. (2021), "Photo-thermoelastic investigation of semiconductor material due to distributed loads", J. Solid Mech., 13(2), 202-212. https://doi.org/10.22034/jsm.2020.1907462.1639.
  38. Sharma, N. and Kumar, R. (2022), "Photothermoelastic deformation in dual phase lag model due to concentrated inclined load", Ital. J. Pure Appl. Math., 48, 1147-1160.
  39. 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/sgce10.4. 10:12720/sgce10.4
  40. Sharma, S. and Khator, S. (2022), "Micro- Grid planning with aggregator's role in the renewable inclusive pro sumer market", J. Power Energy Eng., 10(4), 47-62. https://doi.org/10.4236/jpee.2022-10404.
  41. Sharma, S. and Sharma, K. (2014), "Influence of heat sources and relaxation time on temperature distribution in tissues", Int. J. Appl. Mech. Eng., 19(2), 427-433. https://doi.org/10.2478/ijame-2014-0029.
  42. Sharma, S., Sharma, K. and Bhargava, R.R. (2013), "Effect of viscosity on wave propagation in anisotropic thermoelastic with Green-Naghdi theory type-II and type- III", Mater. Phys. Mech., 16(2), 144-158.
  43. Stearns, R. and Kino, G. (1985), "Effect of electronic strain on photoacoustic generation in silicon", Appl. Phys. Lett., 47(10), 1048-1050. https://doi.org/10.1063/1.96374.
  44. Todorović, D.M. (2003), "Photothermal and electronic elastic effects in microelectromechanical structures", Rev. Scientif. Instrum., 74(1), 578-581. https://doi.org/10.1063/1.1520324.
  45. Todorović, D.M. (2005), "Plasmaelastic and thermoelastic waves in semiconductors", J. Physique IV, 125, 551-555. https://doi.org/10.1051/jp4:2005125127.
  46. Tzou, D.Y. (1995), "A unified approach for heat conduction from macro-to-micro- scales", J. Heat Transf., 117(1), 8-16. https://doi.org/10.1115/1.2822329.
  47. Wang, J. and Li, H. (2011), "Surpassing the fractional derivative: Concept of the memory-dependent derivative", Comput. Math. Appl., 62(3), 1562-1567. https://doi.org/10.1016/j.camwa.2011.04.028.
  48. Yu, Y.J., Hu, W. and Tian, X.G. (2014), "A novel generalized thermoelasticity model based on memorydependent derivative", Int. J. Eng. Sci., 81, 123-134. https://doi.org/10.1016/j.ijengsci.2014.04.014.
  49. Zakaria, K., Sirwah, M.A. and Abouelregal, A.E. (2021), "Photo-thermoelastic model with time-fractional of higher order and phase lags for a semiconductor rotating materials", Silicon, 13, 573-585. https://doi.org/10.1007/s12633-020-00451-z.
  50. Zenkour, A.M. (2020), "Exact coupled solution for photothermal semiconducting beams using a refined multi- phase-lag theory", Opt. Laser Technol., 128, 106233. https://doi.org/10.1016/j.optlastec.2020.106233.