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Thermomechanical interactions of rotating thermoelastic magneto-microelongated medium heated by laser and initially stressed via non-local elasticity and GN III

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Abstract

The present manuscript studies the rotation and initial stress impacts on a magneto-microelongated thermoelastic medium based on Eringen non-local elasticity and Green–Naghdi type III model. The effect of a permanent magnetic field on the studied plane problem was formulated using Lorentz force concept as the laser pulse heating during the study. The harmonic wave solution method was used to calculate the dimensionless strain, local and non-local stresses, temperature, and microelongational scalar. The results obtained were shown numerically and graphically with various cases. The non-local coefficients have a prominent role in changing the studied physical fields. These parameters may become a new indicator and more realistic model according to their ability to conduct the thermal energy in solids. The results obtained in this work may be useful for researchers in the local material science, new material designers, and smart materials. This study is helpful for theoretical modeling of thermoelasticity at the micro-nanoscale and may be beneficial to the design of nano-sized devices.

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References

  1. Eringen, A.C.: Linear theory of non-local elasticity and dispersion of plane waves. Int. J. Eng. Sci. 10, 425–435 (1972)

    Article  MATH  Google Scholar 

  2. Eringen, A.C.: Theory of thermo-microstretch elastic solids. Int. J. Eng. Sci. 28, 1291–1301 (1990)

    Article  MATH  Google Scholar 

  3. Hilal, M.I.M.: Analytical solution of rotation and thermodiffusion of thermoelastic microstretch medium with microtemperatures. J. Brazil Soc. Mech. Sci. Eng. 41, 447–458 (2019)

    Article  Google Scholar 

  4. Shaw, S., Mukhopadhyay, B.: Periodically varying heat source response in a functionally graded microelongated medium. App. Math. Comp. 218, 6304–6313 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  5. Shaw, S., Mukhopadhyay, B.: Moving heat source response in a thermoelastic microelongated solid. J. Eng. Phys. Thermophys 86, 716–722 (2013)

    Article  Google Scholar 

  6. Ailawalia, P., Sachdeva, S.K., Pathania, D.S.: Plane strain deformation in a thermoelastic microelongated solid with internal heat source. Int. J. Appl. Mech. Eng. 20, 717–731 (2015)

    Article  MATH  Google Scholar 

  7. Hilal, M.I.M.: Thermodynamic modeling of a laser pulse heating in a rotating micro-elongated non-local thermoelastic solid due to (G-N) theory. ZAMM-J. Appl. Math. Mech. Zeitschrift für Angewandte Mathematik und Mechanik (2021). https://doi.org/10.1002/zamm.202100285

    Article  Google Scholar 

  8. Hilal, M.I.M.: Response of the: Comments on the paper “Thermodynamic modeling of a laser pulse heating in a rotating microelongated nonlocal thermoelastic solid due to G-N theory, Mohamed I.M. Hilal, ZAMM, 2021, zamm.202100285, zamm. 202100285.R1, by Mohamed I. A. Othman, J. Appl. Math. Mech. ZAMM, https://doi.org/10.1002/zamm.202200003. (2022)

  9. Green, A.E., Naghdi, P.M.: A re-examination of the basic postulates of thermomechanics. Proc. Royal Soc. London A 432, 171–194 (1991)

    MathSciNet  MATH  Google Scholar 

  10. Green, A.E., Naghdi, P.M.: On undamped heat wave in an elastic solid. J. Thermal Stress. 15, 253–264 (1992)

    Article  MathSciNet  Google Scholar 

  11. Green, A.E., Naghdi, P.M.: Thermoelasticity without energy dissipation. J. Elasticity 31, 189–209 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  12. Hetnarski, R.B., Ignaczak, J.: Generalized thermoelasticity. J Thermal. Stress. 22, 451–470 (1999)

    Google Scholar 

  13. Othman, M.I.A., Hilal, M.I.M., Elmaklizi, Y.D.: The effect of gravity and diffusion on micropolar thermoelasticity with temperature-dependent elastic medium under G-N theory. Mech. Mecha. Eng. 21, 657–677 (2017)

    Google Scholar 

  14. Othman, M.I.A., Zidan, M.E.M., Hilal, M.I.M.: The effect of magnetic field on a rotating thermoelastic medium with voids under thermal loading due to laser pulse with energy dissipation. Canad. J. Phys. 92, 1359–1371 (2014)

    Article  Google Scholar 

  15. Othman, M.I., Zidan, M.E., Hilal, M.I.: Effect of gravitational field and temperature dependent properties on two-temperature thermoelastic medium with voids under GN theory. Comput. Mater. Continua 40(3), 179–201 (2014)

    Google Scholar 

  16. Othman, M.I., Zidan, M.E., Hilal, M.I.: The effect of initial stress on thermoelastic rotating medium with voids due to laser pulse heating with energy dissipation. J. Therm. Stress. 38(8), 835–853 (2015)

    Article  Google Scholar 

  17. Hobiny, A., Abbas, I.A.: A GN model on photothermal interactions in a two-dimensions semiconductor half-space. Res. Physic. 15, 102588 (2019)

    Google Scholar 

  18. Jahangir, A., Atwa, S., Rehman, N., Usman, M., Ashraf, M.B., Muhammad, N.: Diffusion effect on plane harmonic waves through thermoelastic microstretch medium in context of Green-Naghdi theory. Indian J. Phys. 94, 987–998 (2020)

    Article  Google Scholar 

  19. Hilal, M.I.M.: Fourier and Laplace transforms in micropolar thermoelastic with rotation and Hall current in case of energy dissipation and thermal shock. Indian J. Phys. 94, 1515–1525 (2020)

    Article  Google Scholar 

  20. Eringen, A.C.: Theory of nonlocal thermoelasticity. Int. J. Eng. Sci. 12, 1063–1077 (1974)

    Article  MATH  Google Scholar 

  21. Eringen, A.C.: Nonlocal Continuum Field Theories. Springer Verlag, New York (2002)

    MATH  Google Scholar 

  22. Clerk-Maxwell, J.: A dynamical theory of the electromagnetic field. Philos. Trans. Roy. Soc. London 155, 459–512 (1865)

    Article  Google Scholar 

  23. Knopoff, L.: The interaction between elastic wave motions and a magnetic field in electrical conductors. J. Geophys. Res. 60, 441–456 (1955)

    Article  Google Scholar 

  24. Chadwick, P.: Elastic wave propagation in a magnetic field. Proc. Int. Conger Appl. Mech. Brussels Belgium 7, 143–153 (1957)

    Google Scholar 

  25. Nayfeh, A.H., Nemat-Nasser, S.: Electromagneto-thermoelastic plane waves in solids with thermal relaxation. J. Appl. Mech. 39, 108–113 (1972)

    Article  MATH  Google Scholar 

  26. Allam, M.N., Elsibai, K.A., Abouelregal, A.E.: Magneto thermoelasticity for an infinite body with a spherical cavity and variable material properties without energy dissipation. Int. J. Solid Struct. 47, 2631–2638 (2010)

    Article  MATH  Google Scholar 

  27. Abouelregal, A.E., Abo-Dahab, S.M.: Dual-phase-lag diffusion model for Thomson’s phenomenon on electromagneto-thermoelastic an infinitely long solid cylinder. J. Comput. Theor. Nanosci. 11, 1031–1039 (2014)

    Article  Google Scholar 

  28. Othman, M.I.A., Tantawi, R.S., Hilal, M.I.M.: Hall current and gravity effect on magneto-micropolar thermoelastic medium with microtemperatures. J. Therm. Stress. 39, 751–771 (2016)

    Article  Google Scholar 

  29. Schoenberg, M., Censor, D.: Elastic waves in rotating media. Quart. Appl. Math. 31, 115–125 (1973)

    Article  MATH  Google Scholar 

  30. Othman, M.I.A., Tantawi, R.S., Hilal, M.I.M.: Rotation and modified Ohm’s law influence on magneto-thermoelastic micropolar material with microtemperatures. Appl. Math. Comput. 276, 468–480 (2016)

    MATH  Google Scholar 

  31. Hilal, M.I.M., Tantawi, R.S., Othman, M.I.A.: The gravity impact in a rotating micropolar thermoelastic medium with microtemperatures. J. Ocean Eng. Sci. 3, 325–333 (2018)

    Article  Google Scholar 

  32. Lotfy, Kh., El-Bary, A.A., Ismail, E.A., Atef, H.A.: Analytical solution of a rotating semiconductor elastic medium due to a refined heat conduction equation with hydrostatic initial stress. Alex. Eng. J. 59, 4947–4958 (2020)

    Article  Google Scholar 

  33. Sun, Y., Fang, D., Saka, M., Soh, A.K.: Laser-induced vibrations of micro-beams under different boundary conditions. Int. J. Solid Struct. 45, 1993–2013 (2008)

    Article  MATH  Google Scholar 

  34. Franco, A., Romoli, L., Musacchio, A.: Modelling for predicting seam geometry in laser beam welding of stainless steel. Int. J. Therm. Sci. 79, 194–205 (2014)

    Article  Google Scholar 

  35. Othman, M.I.A., Hilal, M.I.M.: Propagation of plane waves of magneto-thermoelastic medium with voids influenced by the gravity and laser pulse under G-N theory. Multi. Model. Mater. Struct. 12, 326–344 (2016)

    Article  Google Scholar 

  36. Othman, M.I., Tantawi, R.S., Hilal, M.I.: Laser pulse, initial stress and modified Ohm’s law in micropolar thermoelasticity with microtemperatures. Res. Phys. 8, 642–653 (2018)

    Google Scholar 

  37. Othman, M.I.A., Tantawi, R.S., Hilal, M.I.M.: Laser pulses and rotation effects with the temperature dependent properties in micropolar thermoelastic solids with microtemperatures. Multi. Model. Mater. Struct. 15, 418–436 (2019)

    Article  Google Scholar 

  38. Abo-Dahab, S.M., Abouelregal, A.E., Marin, M.: Generalized thermoelastic functionally graded on a thin slim strip non-Gaussian laser beam. Symmetry 12(7), 1094 (2020)

    Article  Google Scholar 

  39. Hilal, M.I.M.: Reflection waves phenomena in a rotating magneto-micropolarthermoelastic medium with temperature dependency and gravity using Green-Naghdi theory. Mech. Based Des. Struct. Mach. Int. J. (2020). https://doi.org/10.1080/15397734.2020.1807362

    Article  Google Scholar 

  40. Montanaro, A.: On singular surfaces in isotropic linear thermoelasticity with initial stress. J. Acoust. Soc. Am. 106, 1586–1588 (1999)

    Article  Google Scholar 

  41. Wang, J., Slattery, P.: Thermoelasticity without energy dissipation for initially stressed bodies. Int. J. Math. Math. Sci. 31, 329–337 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  42. Abbas, I.A.: Generalized magneto-thermoelasticity in a nonhomogeneous isotropic hollow cylinder using the finite element method. Arch. Appl. Mech. 79, 41–50 (2009)

    Article  MATH  Google Scholar 

  43. Abbas, I.A.: A GN model for thermoelastic interaction in an unbounded fiber-reinforced anisotropic medium with a circular hole. Appl. Math. Lett. 26, 232–239 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  44. Abbas, I.A.: Eigenvalue approach on fractional order theory of thermoelastic diffusion problem for an infinite elastic medium with a spherical cavity. Appl. Math. Model 39, 6196–6206 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  45. Abbas, I.A., Zenkour, A.M.: 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, 331–338 (2014)

    Article  Google Scholar 

  46. Abbas, I.A., Abdallah, A.N., Alzahrani, F., Spagnuolo, M.: Wave propagation in a generalized thermoelastic plate using eigenvalue approach. J. Therm. Stress. 39, 1367–1377 (2016)

    Article  Google Scholar 

  47. Alzahrani, F., Hobiny, A., Abbas, I., Marin, M.: An eigenvalues approach for a two-dimensional porous medium based upon weak, normal and strong thermal conductivities. Symmetry 12(5), 848 (2020). https://doi.org/10.3390/SYM12050848

    Article  Google Scholar 

  48. Abouelregal, A.E., Akgöz, B., Civalek, Ö.: Nonlocal thermoelastic vibration of a solid medium subjected to a pulsed heat flux via Caputo-Fabrizio fractional derivative heat conduction. Appl. Phys. A 128, 660 (2022)

    Article  Google Scholar 

  49. Zenkour, A.M., Abouelregal, A.E.: Magnetothermoelastic interaction in a rod of finite length subjected to moving heat sources via Eringen’s nonlocal model. J. Eng. Phys. Thermophys. 95, 651–651 (2022)

    Article  Google Scholar 

  50. Khalil, K.M., Abouelregal, A.E.: Effect of viscous-Pasternak foundation on laser-excited microbeams via modified thermo-elastic MGT model. J. Ocean Eng. Sci. (2022). https://doi.org/10.1016/j.joes.2022.05.021

    Article  Google Scholar 

  51. Abouelregal, A.E., Alanazi, R., Sedighi, H.M.: Thermal plane waves in unbounded nonlocal medium exposed to a moving heat source with a non-singular kernel and higher order time derivatives. Eng. Anal. Boundary Elem. 140, 564–475 (2022)

    Article  MATH  Google Scholar 

  52. Mohammed, W.W., Abouelregal, A.E., Atta, D., Khelifi, F.: Thermoelastic responses in a nonlocal infinite solid with a circular cylindrical cavity due to a moving heat supply under the MGT model of thermal conductivity. Phys. Scr. 97, 035705 (2022)

    Article  Google Scholar 

  53. Awwad, E., Abouelregal, A.E., Atta, D., Sedighi, H.M.: Photo-thermoelastic behavior of a functionally graded? Semiconductor medium excited by thermal laser pulses. Phys. Scripta 97, 030008 (2022)

    Article  Google Scholar 

  54. Abouelregal, A.E., Mondal, S.: Thermoelastic vibrations in initially stressed rotating microbeams caused by laser irradiation. ZAMM-J. Appl. Math. Mech. Zeitschrift für Angewandte Mathematik und Mechanik 102(4), e202000371 (2022). https://doi.org/10.1002/zamm.202000371

    Article  MathSciNet  Google Scholar 

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  1. Department of Basic Sciences, Faculty of Engineering, Sinai University, Al-Arish, Egypt

    Mohamed I. M. Hilal

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Hilal, M.I.M. Thermomechanical interactions of rotating thermoelastic magneto-microelongated medium heated by laser and initially stressed via non-local elasticity and GN III. Acta Mech 233, 5183–5197 (2022). https://doi.org/10.1007/s00707-022-03385-2

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