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On a Nonlocal Fiber-Reinforced Thermo-Visco-Elastic Solid Via Multi-Phase-Lag Model under the Influence of Gravity

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Abstract

In this paper, an analytical solution for the effect of gravity on fiber-reinforced visco-thermoelastic solids is presented. The analysis and discussion of this study are carried out using the refined phase lag theory. A general solution for the field size can be found using the normal modulus analysis method. Using appropriate boundary conditions calculate the physics and determine the values using MATLAB programming. The results for different gravitational field values and locality are compared. On the other hand, field values for parameters and viscosity with and without fiber-reinforcement were compared.

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DATA AVAILABILITY

Data sharing is not applicable to this paper as no data sets were created or analyzed during the current investigation.

REFERENCES

  1. T. J. J. A. Bromwich, “On the influence of gravity on elastic waves and in particular on the vibrations of an elastic globe,” Proc. London Math. Soc. 30, 98–120 (1898).

    Article  MathSciNet  Google Scholar 

  2. A. E. H. Love, Some Problems of Geodynamics (Dover, New York, 1911).

    Google Scholar 

  3. S. C. Das, D. P. Acharya, and P. R. Sengupta, “Surface waves in an inhomo- geneous elastic medium under the influence of gravity,” Rev. Roum. Des. Sci. Tech. 37, 539–551 (1992).

    Google Scholar 

  4. A. M. Abd-Alla, “Propagation of Rayleigh waves in an elastic half-space of orthotropic material,” Appl. Math Comput. 99, 61–69 (1999). https://doi.org/10.1016/S0096-3003(97)10170-9

    Article  MathSciNet  Google Scholar 

  5. M. I. A. Othman and E. M. Abd-Elaziz, “Effect of rotation on a micropolar magneto-thermoelastic medium with dual-phase-lag model under gravitational field,” Microsys. Tech. 23, 4979–4987 (2017). https://doi.org/10.1007/s00542-017-3295-y

    Article  Google Scholar 

  6. S. M. Said, E. M. Abd-Elaziz, and M. I. A. Othman, “The effect of initial stress and rotation on a nonlocal fiber-reinforced thermoelastic medium with a fractional derivative heat transfer,” ZAMM 102, e202100110 (2022). https://doi.org/10.1002/zamm.202100110

  7. A. Sur, P. Pal, and M. Kanoria, “Modeling of memory-dependent derivative in a fiber-reinforced plate under gravitational effect,” J. Therm. Stress. 41, 973–992 (2018). https://doi.org/10.1080/01495739.2018.1447316

    Article  Google Scholar 

  8. E. A. A. Ahmed, E. E. M. Eraki, and M. I. A. Othman, “Gravity effect in a piezo- thermoelastic diffusive medium with dual-phase-lag model,” Int. J. Comput. Mater. Sci. Eng. 12, 2350008 (2023). https://doi.org/10.1142/S2047684123500082

  9. A. J. Belfield, T. G. Rogers, and A. J. M. Spencer, “Stress in elastic plates reinforced by fiber lying in concentric circles,” J. Mech. Phys. Sol. 31, 25–54 (1983). https://doi.org/10.1016/0022-5096(83)90018-2

    Article  ADS  Google Scholar 

  10. A. Chattopadhyay and S. Choudhury, “Propagation, reflection and transmission of magnetoelastic shear weaves in a self-reinforced medium,” Int. J. Eng. Sci. 28, 485–495 (1990). https://doi.org/10.1016/0020-7225(90)90051-J

    Article  Google Scholar 

  11. S. Deswal, B. S. Punia, and K. K. Kalkal, “Reflection of plane waves at the initially stressed surface of a fiber-reinforced thermoelastic half space with temperature dependent properties,” Int. J. Mech. Mater. Des. 15, 159–173 (2019). https://doi.org/10.1007/s10999-018-9406-9

    Article  Google Scholar 

  12. M. I. A. Othman and S. M. Said, “The effect of rotation on two-dimensional problem of a fiber-reinforced thermoelastic with one relaxation time,” Int. J. Thermophys. 33, 160–171 (2012). https://doi.org/10.1007/s10765-011-1109-5

    Article  ADS  CAS  Google Scholar 

  13. M. I. A. Othman and S. M. Said, “Plane waves of a fiber-reinforcement magneto- thermoelastic comparison of three different theories,” Int. J. Thermophys. 34, 366–383 (2013). https://doi.org/10.1007/s10765-013-1417-z

    Article  ADS  CAS  Google Scholar 

  14. C-B. Xiong, L-N. Yu, and Y-B. Niu, “Effect of variable thermal conductivity on the generalized thermoelasticity problems in a fiber-reinforced anisotropic half- space,” Adv. Mater. Sci. Eng. 2019, 8625371 (2019). https://doi.org/10.1155/2019/8625371

  15. M. I. A. Othman, S. M. Said, and E. M. Abd-Elaziz, “Effect of magnetic field and gravity on thermoelastic fiber-reinforced with memory-dependent derivative, advances in materials research,” Adv. Mater. Resear. 12, 101–118 (2023). https://doi.org/10.12989/amr.2023.12.2.101

    Article  Google Scholar 

  16. A. C. Eringen, “Nonlocal polar elastic continua,” Int. J. Eng. Sci. 10, 1–16 (1972) https://doi.org/10.1016/0020-7225(72)90070-5

    Article  MathSciNet  Google Scholar 

  17. N. Sarkar, S. Mondal, and M. I. A. Othman, “Effect of the laser pulse on transient waves in a non-local thermoelastic medium under Green-Naghdi theory,” Struct. Eng. Mech. 74, 471–479 (2020). https://doi.org/10.12989/sem.2020.74.4.471

    Article  Google Scholar 

  18. X-W. Zhu, Y-B. Wang, and H-H. Dai, “Buckling analysis of Euler–Bernoulli beams using Eringen two-phase nonlocal model,” Int. J. Eng. Sci. 116, 130–140 (2017). https://doi.org/10.1016/j.ijengsci.2017.03.008

    Article  MathSciNet  Google Scholar 

  19. A. C. Eringen, “Theory of nonlocal thermoelasticity,” Int. J. Eng. Sci. 12, 1063–1077 (1974). https://doi.org/10.1016/0020-7225(74)90033-0

    Article  Google Scholar 

  20. M. I. A. Othman, M. Fekry, and M. Marin, “Plane waves in generalized magneto-thermo-viscoelastic medium with voids under the effect of initial stress and laser pulse heating,” Struct. Eng. Mech. 73, 621З629 (2020). https://doi.org/10.12989/sem.2020.73.6.621

    Article  Google Scholar 

  21. A. C. Eringen and D. G. B. Edelen, “On nonlocal elasticity,” Int. J. Eng. Sci. 10, 233–248 (1972). https://doi.org/10.1016/0020-7225(72)90039-0

    Article  MathSciNet  Google Scholar 

  22. A. M. Zenkour, “Nonlocal thermoelasticity theory without energy dissipation for nano-machined beam resonators subjected to various boundary conditions,” Microsys. Technol. 23, 55–65 (2017). https://doi.org/10.1007/s00542-015-2703-4

    Article  Google Scholar 

  23. M. I. A. Othman, S. M. Said, and M. Marin, “A novel model of plane waves of two-temperature fiber-reinforced thermoelastic medium under the effect of gravity with three-phase-lag model,” Int. J. Numer. Methods Heat Fluid Flow. 29, 4788-4806 (2019). https://doi.org/10.1108/HFF-04-2019-0359

    Article  Google Scholar 

  24. P. Luo, X. Li, and X. Tian, “Nonlocal thermoelasticity and its application in thermoelastic problem with temperature-dependent thermal conductivity,” Eur. J. Mech.- A/Solids 87, 104204 (2021). https://doi.org/10.1016/j.euromechsol.2020.104204

  25. T. Saeed and I. A. Abbas, “Effects of the nonlocal thermoelastic model in a thermoelastic nanoscale material,” Math. 10, 284 (2022). https://doi.org/10.3390/math10020284

    Article  Google Scholar 

  26. A. Hobiny and I. A. Abbas, “The effect of a nonlocal thermoelastic model on a thermoelastic material under fractional time derivatives,” Fractal Fractional 6, 639 (2022). https://doi.org/10.3390/fractalfract6110639

    Article  Google Scholar 

  27. A. E. Abouelregal, “A novel model of nonlocal thermoelasticity with time derivatives of higher order,” Math. Methods Appl. Sci. 43, 6746–6760 (2020). https://doi.org/10.1002/mma.6416

    Article  ADS  MathSciNet  Google Scholar 

  28. S. M. Said, E. M. Abd-Elaziz, and M. I. A. Othman, “Effect of gravity and initial stress on a nonlocal thermo-viscoelastic medium with two-temperature and fractional derivative heat transfer,” ZAMM 102, e202100316 (2022). https://doi.org/10.1002/zamm.202100316

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This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.

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Correspondence to Mohamed I.A. Othman, Samia M. Said or Esraa M. Gamal.

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Othman, M.I., Said, S.M. & Gamal, E.M. On a Nonlocal Fiber-Reinforced Thermo-Visco-Elastic Solid Via Multi-Phase-Lag Model under the Influence of Gravity. Mech. Solids 58, 2399–2411 (2023). https://doi.org/10.3103/S0025654423601519

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