Structural Engineering and Mechanics

  • 제80권6호
  • /
  • Pages.669-675
  • /
  • 2021
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

A GN model of thermoelastic interaction in a 2D orthotropic material due to pulse heat flux

  • Hobiny, Aatef (Nonlinear Analysis and Applied Mathematics Research Group (NAAM), Mathematics Department, King Abdulaziz University) ;
  • Abbas, Ibrahim A. (Nonlinear Analysis and Applied Mathematics Research Group (NAAM), Mathematics Department, King Abdulaziz University)
  • 투고 : 2021.05.10
  • 심사 : 2021.09.29
  • 발행 : 2021.12.25
⟨ 이전 논문 다음 논문 ⟩

초록

A GN model with and without energy dissipations is used to discuss the waves propagation in a two-dimension orthotropic half space by the eigenvalues approach. Using the Laplace-Fourier integral transforms to get the solutions of the problem analytically, the basic formulations of the two-dimension problem are given by matrices-vectors differential forms, which are then solved by the eigenvalues scheme. Numerical techniques are used for the inversion processes of the Laplace-Fourier transform. The results for physical quantities are represented graphically. The numerical outcomes show that the characteristic time of pulse heat flux have great impacts on the studied fields values.

키워드

과제정보

This project was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under grant No (DF-054-130-1441). The authors, therefore, gratefully acknowledge the DSR technical and financial support.

참고문헌

  1. Abbas, I. (2006), "Natural frequencies of a poroelastic hollow cylinder", Acta Mechanica, 186(1-4), 229-237. https://doi.org/10.1007/s00707-006-0314-y.
  2. Abbas, I.A. and Alzahrani, F.S. (2016), "Analytical solution of a two-dimensional thermoelastic problem subjected to laser pulse", Steel Compos. Struct., 21(4), 791-803. https://doi.org/10.12989/scs.2016.21.4.791.
  3. Abbas, I.A. and Kumar, R. (2016), "2D deformation in initially stressed thermoelastic half-space with voids", Steel Compos. Struct., 20(5), 1103-1117. https://doi.org/10.12989/scs.2016.20.5.1103.
  4. Abbas, I.A. and Marin, M. (2018), "Analytical solutions of a two-dimensional generalized thermoelastic diffusions problem due to laser pulse", Iran. J. Sci. Technol., Tran. Mech. Eng., 42(1), 57-71. https://doi.org/10.1007/s40997-017-0077-1.
  5. Abbas, I.A. and Zenkour, A.M. (2014), "The effect of rotation and initial stress on thermal shock problem for a fiber-reinforced anisotropic half-space using Green-Naghdi theory", J. Comput. Theor. Nanosci., 11(2), 331-338. https://doi.org/10.1166/jctn.2014.3356.
  6. Abbas, I.A., Alzahrani, F.S. and Elaiw, A. (2019), "A DPL model of photothermal interaction in a semiconductor material", Wav. Rand. Complex Media, 29(2), 328-343. https://doi.org/10.1080/17455030.2018.1433901.
  7. Abd-Elaziz, E.M. and Othman, M.I. (2020), "On a magneto-poro-thermoelastic medium under the influence of the Seebeck effect", Int. J. Numer. Anal. Meth. Geomech., 44(5), 705-719. https://doi.org/10.1002/nag.3039.
  8. Abo-Dahab, S. and Abbas, I.A. (2011), "LS model on thermal shock problem of generalized magneto-thermoelasticity for an infinitely long annular cylinder with variable thermal conductivity", Appl. Math. Model., 35(8), 3759-3768. https://doi.org/10.1016/j.apm.2011.02.028.
  9. Alesemi, M. (2018). "Plane waves in magneto-thermoelastic anisotropic medium based on (L-S) theory under the effect of Coriolis and centrifugal forces", Int. Conf. Mater. Eng. Appl., 348(1), 012018. https://doi.org/10.1088/1757-899X/348/1/012018.
  10. Biot, M.A. (1956), "Thermoelasticity and irreversible thermodynamics", J. Appl. Phys., 27(3), 240-253. https://doi.org/10.1063/1.1722351.
  11. Biswas, S. and Abo-Dahab, S. (2020), "Electro-magneto-thermoelastic interactions in initially stressed orthotropic medium with Green-Naghdi model type-III", Mech. Bas. Des. Struct. Mach., 1-16. https://doi.org/10.1080/15397734.2020.1815212.
  12. Das, N.C., Lahiri, A. and Giri, R.R. (1997), "Eigenvalue approach to generalized thermoelasticity", Ind. J. Pure Appl. Math., 28(12), 1573-1594.
  13. Debnath, L. and Bhatta, D. (2014), Integral Transforms and Their Applications, Chapman and Hall/CRC.
  14. Dhaliwal, R.S. and Sherief, H.H. (1980), "Generalized thermoelasticity for anisotropic media", Quart. Appl. Math., 38(1), 1-8. https://doi.org/10.1090/qam/575828.
  15. El-Naggar, A., Kishka, Z., Abd-Alla, A., Abbas, I., Abo-Dahab, S. and Elsagheer, M. (2013), "On the initial stress, magnetic field, voids and rotation effects on plane waves in generalized thermoelasticity", J. Comput. Theor. Nanosci., 10(6), 1408-1417. https://doi.org/10.1166/jctn.2013.2862.
  16. Elsibai, K.A. and Youssef, H.M. (2011), "State-space approach to vibration of gold nano-beam induced by ramp type heating without energy dissipation in femtoseconds scale", J. Therm. Stress., 34(3), 244-263. https://doi.org/10.1080/01495739.2010.545737.
  17. Ezzat, M. and El-Bary, A. (2017), "Fractional magneto-thermoelastic materials with phase-lag Green-Naghdi theories", Steel Compos. Struct., 24(3), 297-307. http://doi.org/10.12989/scs.2017.24.3.297.
  18. Green, A. and Naghdi, P. (1992), "On undamped heat waves in an elastic solid", J. Therm. Stress., 15(2), 253-264. https://doi.org/10.1080/01495739208946136.
  19. Green, A. and Naghdi, P. (1993), "Thermoelasticity without energy dissipation", J. Elast., 31(3), 189-208. https://doi.org/10.1007/BF00044969.
  20. 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.
  21. Hobiny, A. and Abbas, I.A. (2018), "Analytical solutions of photo-thermo-elastic waves in a non-homogenous semiconducting material", Result. Phys., 10, 385-390. https://doi.org/10.1016/j.rinp.2018.06.035.
  22. Hobiny, A.D. and Abbas, I.A. (2017), "A study on photothermal waves in an unbounded semiconductor medium with cylindrical cavity", Mech. Time-Depend. Mater., 21(1), 61-72. https://doi.org/10.1007/s11043-016-9318-8.
  23. Kar, A. and Kanoria, M. (2009), "Generalized thermoelastic functionally graded orthotropic hollow sphere under thermal shock with three-phase-lag effect", Eur. J. Mech.-A/Solid., 28(4), 757-767. https://doi.org/10.1016/j.euromechsol.2009.01.003.
  24. Karimi Zeverdejani, P. and Kiani, Y. (2020), "Nonlinear generalized thermoelasticity of FGM finite domain based on Lord-Shulman theory", Wav. Rand. Complex Media, 1-22. https://doi.org/10.1080/17455030.2020.1788746.
  25. Kaur, H. and Lata, P. (2020), "Effect of thermal conductivity on isotropic modified couple stress thermoelastic medium with two temperatures", Steel Compos. Struct., 34(2), 309-319. https://doi.org/10.12989/scs.2020.34.2.309.
  26. Kaur, I. and Lata, P. (2020), "Axisymmetric deformation in transversely isotropic magneto-thermoelastic solid with Green- Naghdi III due to inclined load", Int. J. Mech. Mater. Eng., 15(1), 1-9. https://doi.org/10.1186/s40712-019-0111-8.
  27. Khan, A.A., Bukhari, S.R., Marin, M. and Ellahi, R. (2019), "Effects of chemical reaction on third-grade MHD fluid flow under the influence of heat and mass transfer with variable reactive index", Heat Transf. Res., 50(11), 1061-1080. https://doi.org/10.1615/HeatTransRes.2018028397.
  28. Lata, P. (2018), "Effect of energy dissipation on plane waves in sandwiched layered thermoelastic medium", Steel Compos. Struct., 27(4), 439-451. http://doi.org/10.12989/scs.2018.27.4.439.
  29. Lata, P. and Kaur, I. (2019), "Effect of rotation and inclined load on transversely isotropic magneto thermoelastic solid", Struct. Eng. Mech., 70(2), 245-255. http://doi.org/10.12989/sem.2019.70.2.245.
  30. Lata, P. and Kaur, I. (2019), "Effect of time harmonic sources on transversely isotropic thermoelastic thin circular plate", Geomech. Eng., 19(1), 29-36. http://doi.org/10.12989/gae.2019.19.1.029.
  31. Lata, P. and Kaur, I. (2019), "Thermomechanical interactions in transversely isotropic magneto thermoelastic solid with two temperatures and without energy dissipation", Steel Compos. Struct., 32(6), 779-793. http://doi.org/10.12989/scs.2019.32.6.779.
  32. Lata, P. and Singh, S. (2020), "Deformation in a nonlocal magneto-thermoelastic solid with hall current due to normal force", Geomech. Eng., 22(2), 109. http://doi.org/10.12989/gae.2020.22.2.109.
  33. Lata, P. and Singh, S. (2021), "Stoneley wave propagation in nonlocal isotropic magneto-thermoelastic solid with multi-dual-phase lag heat transfer", Steel Compos. Struct., 38(2), 141. http://doi.org/10.12989/scs.2021.38.2.141.
  34. Lata, P., Kumar, R. and Sharma, N. (2016), "Plane waves in an anisotropic thermoelastic", Steel Compos. Struct., 22(3), 567-587. http://doi.org/10.12989/scs.2016.22.3.567.
  35. 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.
  36. Marin, M. (1999), "An evolutionary equation in thermoelasticity of dipolar bodies", J. Math. Phys., 40(3), 1391-1399. https://doi.org/10.1063/1.532809.
  37. MArin, M., Baleanu, D. and Vlase, S. (2017), "Effect of microtemperatures for micropolar thermoelastic bodies", Struct. Eng. Mech., 61(3), 381-387. http://doi.org/10.12989/sem.2017.61.3.381.
  38. Marin, M., Vlase, S. and Paun, M. (2015), "Considerations on double porosity structure for micropolar bodies", AIP Adv., 5(3), 037113. https://doi.org/10.1063/1.4914912.
  39. Othman, M.I., Alharbi, A.M. and Al-Autabi, A.-A.M.K. (2020), "Micropolar thermoelastic medium with voids under the effect of rotation concerned with 3PHL model", Geomech. Eng., 21(5), 447-459. http://doi.org/10.12989/gae.2020.21.5.447.
  40. Saeed, T., Abbas, I. and Marin, M. (2020), "A gl model on thermos-elastic interaction in a poroelastic material using finite element method", Symmetry, 12(3), 488. https://doi.org/10.3390/sym12030488.
  41. Sarkar, N., Mondal, S. and Othman, M.I. (2020), "Effect of the laser pulse on transient waves in a non-local thermoelastic medium under Green-Naghdi theory", Struct. Eng. Mech., 74(4), 471-479. http://doi.org/10.12989/sem.2020.74.4.471.
  42. Singh, B. (2007), "Wave propagation in a generalized thermoelastic material with voids", Appl. Math. Comput., 189(1), 698-709. https://doi.org/10.1016/j.amc.2006.11.123.
  43. Singh, B. and Pal, S. (2020), "Magneto-thermoelastic interaction with memory response due to laser pulse under Green-Naghdi theory in an orthotropic medium", Mech. Bas. Des. Struct. Mach., 1-18. https://doi.org/10.1080/15397734.2020.1798780.
  44. Stehfest, H. (1970), "Algorithm 368: Numerical inversion of Laplace transforms [D5]", Commun. ACM, 13(1), 47-49. https://doi.org/10.1145/361953.361969.
  45. Vlase, S., Marin, M., Ochsner, A. and Scutaru, M. (2019), "Motion equation for a flexible one-dimensional element used in the dynamical analysis of a multibody system", Contin. Mech. Thermodyn., 31(3), 715-724. https://doi.org/10.1007/s00161-018-0722-y.
  46. Zenkour, A.M. and Abbas, I.A. (2014), "Magneto-thermoelastic response of an infinite functionally graded cylinder using the finite element method", J. Vib. Control, 20(12), 1907-1919. https://doi.org/10.1177/1077546313480541.
  47. Zenkour, A.M. and Abbas, I.A. (2014), "Nonlinear transient thermal stress analysis of temperature-dependent hollow cylinders using a finite element model", Int. J. Struct. Stab. Dyn., 14(07), 1450025. https://doi.org/10.1142/S0219455414500254.
  48. Zenkour, A.M. and Abbas, I.A. (2014), "Thermal shock problem for a fiber-reinforced anisotropic half-space placed in a magnetic field via G-N model", Appl. Math. Comput., 246 482-490. https://doi.org/10.1016/j.amc.2014.08.052.