Abstract
Here, we study the effect of rotation and diffusion on a thermoelastic plate with four-phase lag. The normal mode method was used to get the exact solution of the displacement, stress, and temperature functions. The last-mentioned functions were plotted and comprised in three cases, presence and absence of rotation, in addition to the context of three cases, and finally in the presence and absence of laser pulse.
REFERENCES
M. Biot, “Thermoelasticity and irreversible thermodynamics,” J. Appl. Phys. 27, 240–253 (1956). https://doi.org/10.1063/1.1722351
H. W. Lord and Y. Shulman, “A generalized dynamical theory of thermoelasticity,” J. Mech. Phys. Solid 15, 299–309 (1967). https://doi.org/10.1016/0022-5096(67)90024-5
W. Nowacki, “Dynamical problems of thermoelastic diffusion in solids,” Bull. Polish Ac. Sci. Ser., Sci. Technol. 22, 55–64 (1974).
W. Nowacki, “Dynamical problems of thermoelastic diffusion in elastic solids,” Proc. Vib. Prob. 15, 105–128 (1974).
W. Nowacki, “Dynamical problems of thermoelastic diffusion in solids II,” Bull. Polish Ac. Sci. Ser., Sci. Technol. 22, 129–135 (1974).
W. Nowacki, “Dynamical problems of thermoelastic diffusion in solids III,” Bull. Polish Ac. Sci. Ser., Sci. Technol. 22, 257–266 (1974).
H. H. Sherief, F. Hamza, and H. A. Saleh, “The theory of generalized thermoelastic diffusion,” Int. J. Eng. Sci. 42, 591–608 (2004).
Kh. Lotfy, “A novel model of magneto photothermal diffusion (MPD) on polymer nano-composite semiconductor with initial stress,” Waves Random Complex Media. 31 (1), 81-100 (2019). https://doi.org/10.1080/17455030.2019.1566680
A. Bajpai, P. K. Sharma, and R. Kumar, “Modeling of thermoelastic diffusion plate under two temperature, fractional- order, and temperature-dependent material properties,” ZAMM 101 (10), e202000321 (2021). https://doi.org/10.1002/zamm.202000321
M. I. M. Hilal, “Diffusion, rotation, and lagging behavior of a thermoelastic micropolar medium with voids and temperture gradient under mechanical pressure,” Waves Random Complex Media (2021). https://doi.org/10.1080/17455030.2021.2011987
D. Y. Tzou, “Unified field approach for heat conduction from macro-to micro-scales,” J. Heat Transf. 117, 8–16 (1995).
S. K. Roychoudhuri, “On thermoelastic three phase lag model,” J. Therm. Stress. 30, 231–238 (2007).
R. Quintanilla and R. Racke, “A note on stability in three-phase-lag heat conduction,” Int. J. Heat Mass Trans. 51, 24–29 (2008).
I. Abbas, F. Alzahrani, and A. Elaiw, “A DPL model of photothermal interaction in a semiconductor material,” Waves Random Complex Media 29 (2), 328–343 (2019).
Kh. Lotfy, “The elastic wave motions for a photothermal medium of a dual-phase-lag model with an internal heat source and gravitational field,” Can. J. Phys. 94, 400–409 (2016). https://doi.org/10.1139/cjp-2015-0782
M. Marin, “A domain of influence theorem for microstretch elastic materials,” Nonlinear Anal.: Real World Appl. 11 (5), 3446–3452 (2010). https://doi.org/10.1016/j.nonrwa.2009.12.005
M. Marin, “A partition of energy in thermoelasticity of microstretch bodies,” Nonlinear Anal.: Real World Appl. 11 (4), 2436–2447 (2010). https://doi.org/10.1016/j.nonrwa.2009.07.014
Sarhan Y. Atwa, M. K. Ammar, and Eman Ibrahim, “The effect of two- temperature on thermoelastic medium with diffusion due to three phase- lag model,” Appl. Math. Nonlin. Sci. 2 (1), 259–270 (2017). https://doi.org/10.21042/AMNS.2017.1.00022
M. A. Abdou, E. M. Abo- Eldahab, M. K. Ammar, and E. Ibrahim, “New model for discussing the diffusion phenomena effect on a thermoelastic plate associated with three- phase- lag,” Informat. Sci. Lett. 11 (6), 2159–2166 (2022).
A. Hobiny and I. Abbas, “Generalized thermo-diffusion interaction in elastic medium under temperture dependent diffusivity and thermal conductivity,” Mathematics 10 (15), 2773 (2022). https://doi.org/10.3390/math10152773
K.A. Aldwoah, Kh. Lotfy, A. Mhemdi, and A. El-Bary, “A novel magneto-photo-elasto-thermodiffusion electrons- holes model of excited semiconductor,” Case Studies Thermal Eng. 32, 101877 (2022). doi.org/https://doi.org/10.1016/j.csite.2022.101877
M. I. A. Othman, S. Y. Atwa, A. Jahangir, and A. Khan, “The effect of rotation on plane waves in generalized thermo- microstretch elastic solid for a mode- I crack under Green Naghdi theory,” J. Computat. Theor. Nanosci. 12, 1–10 (2015).
M. I. A. Othman and S. Y. Atwa, “2- D problem of anistropic rotating thermoelastic half- space under Green- Naghdi theory,” J. Comutat. Theor. Nanosci. 12, 1363–3270 (2015).
S. Y. Atwa and Eman Ibrahim, “Two temperture effect on a rotational themoelastic medium with diffusion due to three- phase- lag model,” J. Nanotechnol. Adv. Mater. 1, 1–15 (2019).
A. M. H. Yahya, A. E. Abouelregal, K. M. Khalil, and D. Atta, “Thermoelastic response in rotating nanomeams with variable physical properties due to periodic pulse heating,” Case Study Therm. Eng. 28, 101443 (2021). https://doi.org/10.1016/j.csite.2021.101443
I. Kaur, K. Singh, and E-M. Craciun, “A mathematical study of a semiconducting thermoelastic rotating solid cylinder with modified Moore- Gibson- Thompson heat transfer under the hall effect,” Mathematics 10 (14), 2386 (2022). https://doi.org/10.3390/math10142386
M. I. A. Othman, “Effect of thermal loading due to laser pulse on 3-D problem on micropolar thermoelastic solid with energy dissipation,” Mech. Mechanical Eng. 21, 679–701 (2017).
A. Mahdy, Kh. Lotfy, A. El-Bary, and I. Tayel, “Variable thermal conductivity and hyperbolic two-temperature theory during magneto-photothermal theory of semiconductor induced by laser pulses,” Eur. Phys. J. Plus. 136, 651 (2021). doi.org/https://doi.org/10.1140/epjp/s13360-021-01633-3
A. Mahdy, Kh. Lotfy, A. El-Bary, and H. Sarhan, “Effect of rotation and magnetic field on a numerical-refined heat conduction in a semiconductor medium during photo-excitation processes,” Eur. Phys. J. Plus. 136, 553 (2021). doi.org/https://doi.org/10.1140/epjp/s13360-021-01552-3
A. K. Khamis, A. A. El-Bary, Kh. Lotfy, and Allal Bakali, “Photothermal excitation processes with refined multi dual phase-lags theory for semiconductor elastic medium,” Alexandria Eng. J. 59 (1), 1–9 (2020). doi.org/https://doi.org/10.1016/j.aej.2019.11.016
I. M. Tayel, Kh. Lotfy, Alaa A. Al-Bary, et al., “Microelongated thermo-elastodiffusive waves of excited semiconductor material under laser pulses impact,” Mathematics 11 (7), 1627 (2023). https://doi.org/10.3390/math11071627
W. Alhejaili, M. A. El Nasr, Kh. Lotfy, and A. El- Bary, “Laser short-pulse effect on magneto-photo-elasto-thermodiffusion waves of fractional heat equation for non-local excited semiconductor,” Opt. Quantum Electron. 54, 833 (2022). https://doi.org/10.1007/s11082-022-04247-w
A. E. Abouelregal, “Generalized mathematical novel model of thermoelastic diffusion with four phase lags and higher- order time derivative,” Eur. Phys. J. Plus 135, 263 (2020). https://doi.org/10.1140/epjp/s13360-020-00282-2
A. E. Abouelregal, “Modified fractional thermoelasticity model with multi-relaxation times of higher order: application to spherical cavity exposed to a harmonic varying heat,” Waves Random Complex Media 31 (5), 812–832 (2021). https://doi.org/10.1080/17455030.2019.1628320
M. Marin, “A temporally evolutionary equation in elasticity of micropolar bodies with voids,” UPB Sci. Bull. A: Appl. Math. Phys. 60 (3–4), 3–12 (1998).
I. Abbas, A. Hobiny, and M. Marin, “Photo-thermal interactions in a semi-conductor material with cylindrical cavities and variable thermal conductivity,” J. Taibah Univ. Sci. 14 (1), 1369–1376 (2020). https://doi.org/https://doi.org/10.1080/16583655.2020.1824465
M. Marin, A. Seadawy, S. Vlase, and A. Chirila, “On mixed problem in thermoelasticity of type III for Cosserat media,” J. Taibah Univ. Sci. 16 (1), 1264–1274 (2022). https://doi.org/10.1080/16583655.2022.2160290
S. M. Abo-Dahab, A. E. Abouelregal, and M. Marin, “Generalized thermoelastic functionally graded on a thin slim strip non-Gaussian laser beam,” Symmetry 12 (7), 1094 (2020). https://doi.org/10.3390/sym12071094
M. 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 (6), 621–629 (2020). https://doi.org/10.12989/sem.2020.73.6.621
ACKNOWLEDGMENT
The authors extend their appreciation to Princess Nourah bint Abdulrahman University for fund this research under Researchers Supporting Project number (PNURSP2023R154) Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.
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Ibrahim, E., El-Sapa, S., Chteoui, R. et al. Four-Phase Lags in a Generalized Thermoelastic Rotational Diffusive Plate with Laser Pulse Emission. Mech. Solids 58, 2412–2423 (2023). https://doi.org/10.3103/S0025654423601787
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DOI: https://doi.org/10.3103/S0025654423601787