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Nonlocal thermoelastic vibration of a solid medium subjected to a pulsed heat flux via Caputo–Fabrizio fractional derivative heat conduction

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Abstract

An advanced model is developed to analyze the thermoelastic vibrations of a nonlocal isotropic solid medium subjected to a pulsed heat flux using Caputo–Fabrizio fractional derivative heat conduction. The mathematical model of an infinite isotropic and homogeneous medium is obtained by applying nonlocal elasticity theory and fractional calculus using single kernels with generalized thermoelasticity. The Laplace transform technique is employed to numerically solve the fundamental equations under the corresponding boundary conditions of the problem. A detailed parametric study is performed to examine the effects of increasing laser pulse duration as well as fractional and nonlocal order coefficients on thermoelastic waves of the medium. It can be emphasized that the higher temperature will reduce the thermal conductivity. It is also notable that some special cases and previous thermoelastic models can be reduced from the present model.

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References

  1. J.K. Chen, J.E. Beraun, C.L. Tham, Int. J. Eng. Sci. 42, 793–807 (2004)

    Google Scholar 

  2. X. Wang, X. Xu, Appl. Phys. A. 73, 107–114 (2001)

    ADS  Google Scholar 

  3. D.Y. Tzou, Macro- to Microscale Heat Transfer—The Lagging Behavior (Taylor and Francis, Washington, 1996)

    Google Scholar 

  4. S.I. Anisimov, B.L. Kapeliovich, T.L. Perel’man, Soviet Phys. JETP. 39, 375–377 (1974).

  5. T.Q. Qiu, C.L. Tien, J. Heat Transf. 115, 835–841 (1993)

    Google Scholar 

  6. A.S. Dogonchi, D.D. Ganji, Appl. Therm. Eng. 103, 705–712 (2016)

    Google Scholar 

  7. W. Nowacki, Proc. Vib. Probl. 15, 105–128 (1974)

    Google Scholar 

  8. W. Nowacki, Dynamic Problems of Thermoelasticity (Noordhoff, Netherlands, 1975)

    MATH  Google Scholar 

  9. H.W. Lord, Y. Shulman, J. Mech. Phys. Solid 15, 299–309 (1967)

    ADS  Google Scholar 

  10. I. Podlubny, Fractional Differential Equations (Academic Press, San Diego, 1999)

    MATH  Google Scholar 

  11. S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional Integrals and Derivatives: Theory and Applications (Taylor & Francis, London, 2002)

    MATH  Google Scholar 

  12. B. Ross, A brief history and exposition of the fundamental theory of fractional calculus, in Fractional Calculus and Its Applications, Lecture Notes in Mathematics. ed. by B. Ross (Springer, Heidelberg, 1975)

    Google Scholar 

  13. D. Baleanu, K. Diethelm, E. Scalas, J.J. Trujillo, Fractional Calculus: Models and Numerical Methods (World Scientific, Singapore, 2012)

    MATH  Google Scholar 

  14. V.V. Uchaikin, Fractional Derivatives for Physicists and Engineers (Springer, Berlin, 2013)

    MATH  Google Scholar 

  15. M. Caputo, M. Fabrizio, Prog. Fract. Differ. Appl. 1, 73–85 (2015)

    Google Scholar 

  16. M. Caputo, M. Fabrizio, Meccanica 52, 3043–3052 (2017)

    MathSciNet  Google Scholar 

  17. S.A. Faghidian, J. Press. Vessel. Technol. 139, 031205 (2017)

    Google Scholar 

  18. J. Losada, J. Nieto, Prog. Fract. Differ. Appl. 1, 87–92 (2015)

    Google Scholar 

  19. M. Al-Refai, T. Abdeljawad, Adv. Differ. Equ. 315, (2017).

  20. A. Atangana, Appl. Math. Comput. 273, 948–956 (2016)

    MathSciNet  Google Scholar 

  21. T. Kaczorek, K. Borawski, Int. J. Appl. Math. Comput. Sci. 26, 533–541 (2016)

    MathSciNet  Google Scholar 

  22. B.S.T. Alkahtani, A. Atangana, Chaos Solitons Fractal. 89, 539–546 (2016)

    ADS  Google Scholar 

  23. N. Al-Salti, E. Karimov, K. Sadarangani, Prog. Fract. Differ. Appl. 2, 257–263 (2016)

    Google Scholar 

  24. M. Caputo, M. Fabrizio, Prog. Fract. Differ. Appl. 2, 1–11 (2016)

    Google Scholar 

  25. J.F. Gómez-Aguilar, L. Torres, H. Yépez-Martínez, D. Baleanu, Adv. Differ. Equ. 1, 173 (2016)

    Google Scholar 

  26. E.F.D. Goufo, Math. Model. Anal. 21, 188–198 (2016)

    MathSciNet  Google Scholar 

  27. W. Sparagen, G.E. Claussen, Weld J. 16, 4–10 (1937)

    Google Scholar 

  28. S. Bezzina, A.M. Zenkour, Waves Random Complex Media (2021) https://doi.org/10.1080/17455030.2021.1959670

  29. A.E. Abouelregal, H.M. Sedighi, Appl. Phys. A 127, 582 (2021)

    ADS  Google Scholar 

  30. A.E. Abouelregal, H. Ersoy, Ö. Civalek, Math. 9, 1536 (2021)

    Google Scholar 

  31. R. Tiwari, R. Kumar, A.E. Abouelregal, Appl. Phys. A 128, 160 (2022)

    ADS  Google Scholar 

  32. H.H. Sherief, F.A. Hamza, H.A. Saleh, Int. J. Eng. Sci. 42, 591–608 (2004)

    Google Scholar 

  33. A.E. Abouelregal, D. Atta, Appl. Phys. A 128, 118 (2022)

    ADS  Google Scholar 

  34. E. Abouelregal, H.M. Sedighi, Proc. Inst. Mech. Eng. Part L J. Mater. Des. Appl. 235, 1004–1020 (2021)

    Google Scholar 

  35. L. Knopoff, J. Geophys. Res. 60, 441–456 (1955)

    ADS  Google Scholar 

  36. S. Kaliski, J. Petykiewicz, Proc. Vib. Probl. 4, 1–12 (1959)

    Google Scholar 

  37. P. Chadwick, Proc. Int. Congr. Appl. Mech. 7, 143–153 (1957)

    Google Scholar 

  38. A.H. Nayfeh, S. Nemat-Nasser, J. Appl. Mech. 39, 108–113 (1972)

    ADS  Google Scholar 

  39. M.N. Allam, K.A. Elsibai, A.E. Abouelregal, Int. J. Solid. Struct. 47, 2631–2638 (2010)

    Google Scholar 

  40. A.E. Abouelregal, S.M. Abo-Dahab, J. Therm. Stress. 35, 820–841 (2012)

    Google Scholar 

  41. A.E. Abouelregal, S.M. Abo-Dahab, J. Comput. Theor. Nanosci. 11, 1031–1039 (2014)

    Google Scholar 

  42. A.E. Abouelregal, SILICON 12, 2837–2850 (2020)

    Google Scholar 

  43. A.E. Abouelregal, H. Ahmad, S.W. Yao, Materials 13, 3953 (2020)

    ADS  Google Scholar 

  44. A.C. Eringen, Int. J. Eng. Sci. 10, 1–16 (1972)

    Google Scholar 

  45. A.C. Eringen, D.G.B. Edelen, Int. J. Eng. Sci. 10, 233–248 (1972)

    Google Scholar 

  46. A.C. Eringen, J. Appl. Phys. 54, 4703–4710 (1983)

    ADS  Google Scholar 

  47. J. Peddieson, R. Buchanan, R.P. McNitt, Int. J. Eng. Sci. 41, 305–312 (2003)

    Google Scholar 

  48. J.N. Reddy, Int. J. Eng. Sci. 45, 288–307 (2007)

    Google Scholar 

  49. A.E. Abouelregal, W.W. Mohammed, Math. Method. Appl. Sci. (2020) https://doi.org/10.1002/mma.6764.

  50. A.E. Abouelregal, M. Marin, Symmetry. 12, 1276 (2020)

    Google Scholar 

  51. A.E. Abouelregal, Math. Methods Appl. Sci. (2020). https://doi.org/10.1002/mma.6416

    Article  MathSciNet  Google Scholar 

  52. A.E. Abouelregal, H.M. Sedighi, S.A. Faghidian, A.H. Shirazi, Facta Univ. Ser. Mech. Eng. 19, 633–656 (2021)

    Google Scholar 

  53. K.M. Liew, Y. Zhang, L.W. Zhang, J. Model Mech. Mater. 1, 20160159 (2017)

    Google Scholar 

  54. K. Rajneesh, M. Aseem, R. Rekha, Mediterr. J. Model. Simul. 9, 25–42 (2018)

    Google Scholar 

  55. A.E. Abouelregal, B.O. Mohamed, J. Comput. Theor. Nanosci. 15, 1233–1242 (2018)

    Google Scholar 

  56. B. Akgöz, Ö. Civalek, Int. J. Mech. Sci. 99, 10–20 (2016)

    Google Scholar 

  57. H.M. Numanoğlu, H. Ersoy, B. Akgöz, Ö. Civalek, Math. Method. Appl. Sci. 45, 2592–2614 (2022)

    ADS  Google Scholar 

  58. S. Dastjerdi, B. Akgöz, Ö. Civalek, Int. J. Eng. Sci. 149, 103236 (2020)

    Google Scholar 

  59. A.E. Abouelregal, J. Comput. Appl. Mech. 50, 118–126 (2019)

    Google Scholar 

  60. H.M. Numanoğlu, B. Akgöz, Ö. Civalek, Int. J. Eng. Sci. 130, 33–50 (2018)

    Google Scholar 

  61. R. Barretta, S.A. Faghidian, R. Luciano, Mech. Adv. Mat. Struct. 26, 1307–1315 (2019)

    Google Scholar 

  62. Ö. Civalek, B. Uzun, M.Ö. Yaylı, B. Akgöz, Eur. Phys. J. Plus. 135, 381 (2020)

    Google Scholar 

  63. S.A. Faghidian, J. Comput. Des. Eng. 8(3), 949–959 (2021)

    MathSciNet  Google Scholar 

  64. S.A. Faghidian, Eur. Phys. J. Plus. 136, 559 (2021)

    Google Scholar 

  65. S.A. Faghidian, Math. Meth. Appl. Sci. 1–23 (2020) https://doi.org/10.1002/mma.6885

  66. S.A. Faghidian, Math. Meth. Appl. Sci.1–17 (2020) https://doi.org/10.1002/mma.6877

  67. S.A. Faghidian, K.K. Żur, J.N. Reddy, Int. J. Eng. Sci. 170, 103603 (2022)

    Google Scholar 

  68. A. Atangana, J.F. Gómez-Aguilar, Numer. Methods Partial Differ. Equ. 34, 1502–1523 (2018)

    Google Scholar 

  69. K.M. Furati, M.D. Kassim, N.T. Tatar, Comput. Math. Appl. 64, 1616–1626 (2012)

    MathSciNet  Google Scholar 

  70. P. Veeresha, D.G. Prakasha, H.M. Baskonus, Chaos 29, 013119 (2019)

    MathSciNet  ADS  Google Scholar 

  71. A. Shaikh, A. Tassaddiq, K.S. Nisar, D. Baleanu, Adv. Differ. Equ. 2019, 178 (2019)

    Google Scholar 

  72. J. Losada, J.J. Nieto, Progr. Fract. Differ. Appl. 1, 87–92 (2015)

    Google Scholar 

  73. N. Noda, Thermal stresses in materials with temperature-dependent properties, in Thermal Stress I. ed. by R.B. Hetnarski (Elsevier, Amsterdam, 1986)

    Google Scholar 

  74. G. Honig, U. Hirdes, J. Comput. Appl. Math. 10, 113–132 (1984)

    MathSciNet  Google Scholar 

  75. Q. Wang, K.M. Liew, Phys. Lett. A. 363, 236–242 (2007)

    ADS  Google Scholar 

  76. H.H. Sherief, F.A. Hamza, Meccanica 51, 551–558 (2016)

    MathSciNet  Google Scholar 

  77. Y. Wang, D. Liu, Q. Wang, J. Zhou, Acta Mech. Solid. Sin. 28, 682–692 (2015)

    Google Scholar 

  78. I. Arias, J.D. Achenbach, Int. J. Solid. Struct. 40, 6917–6935 (2003)

    Google Scholar 

  79. F.A. McDonald, Appl. Phys. Lett. 56, 230–232 (1990)

    ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, College of Science and Arts, Jouf University, Al-Qurayyat, Saudi Arabia

    Ahmed E. Abouelregal

  2. Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt

    Ahmed E. Abouelregal

  3. Department of Civil Engineering, Faculty of Engineering, Akdeniz University, Antalya, Turkey

    Bekir Akgöz & Ömer Civalek

  4. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan

    Ömer Civalek

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  1. Ahmed E. Abouelregal
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  2. Bekir Akgöz
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  3. Ömer Civalek
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Correspondence to Bekir Akgöz.

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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). https://doi.org/10.1007/s00339-022-05786-5

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