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Numerical Heat Transfer, Part A: Applications
An International Journal of Computation and Methodology
Volume 82, 2022 - Issue 7
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Articles

Homotopy perturbation method on wave propagation in a transversely isotropic thermoelastic two-dimensional plate with gravity field

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Pages 398-410 | Received 16 Nov 2021, Accepted 12 May 2022, Published online: 15 Jun 2022

References

  • M. A. Biot, “Thermoelasticity and irreversible thermodynamics,” J. Appl. Phys., vol. 27, no. 3, pp. 240–253, 1956. DOI: 10.1063/1.1722351.
  • H. Deresiewicz, “Corrections and additions: effect of boundaries on waves in a thermoelastic solid,” J. Mech. Phys. Solids, vol. 10, no. 2, pp. 179–181, 1962. DOI: 10.1016/0022-5096(62)90020-0.
  • A. E. Green and A. Lindsay, “Thermoelasticity,” J. Elasticity, vol. 2, no. 1, pp. 1–7, 1972. DOI: 10.1007/BF00045689.
  • R. S. Dhaliwal and A. Singh, Dynamic Coupled Thermoelasticity. New Delhi, India: Hindustan Publ. Corp, 1980, pp. 726
  • R. B. Hetnarski and J. Ignaczak, “Generalized thermoelasticity,” J. Therm. Stresses, vol. 22, pp. 451–476, 1999.
  • A. E. Green and P. M. Naghdi, “On undamped heat waves in an elastic solid,” J. Therm. Stresses, vol. 15, no. 2, pp. 253–264, 1992. DOI: 10.1080/01495739208946136.
  • M. Ezzat, M. Othman, and A. El-Karamany, “Electromagneto-thermoelastic plane waves with thermal relaxation in a medium of perfect conductivity,” J. Therm. Stresses, vol. 24, pp. 411–432, 2001.
  • W. E. Warren and P. J. Chen, “Wave propagation in the two temperature theory of thermoelasticity,” J. Acta Mechanica, vol. 16, no. 1–2, pp. 21–33, 1973. DOI: 10.1007/BF01177123.
  • H. M. Youssef, “Theory of two temperature generalized thermoelasticity,” J. Appl. Math., vol. 71, no. 3, pp. 383–390, 2006. DOI: 10.1093/imamat/hxh101.
  • H. M. Youssef and E. A. AI-Lehaibi, “State space approach of two temperature generalized thermoelasticity of one dimensional problem,” Int. J. Solids Struct., vol. 44, no. 5, pp. 1550–1562, 2007. DOI: 10.1016/j.ijsolstr.2006.06.035.
  • D. S. Chandrasekharaiah, “Thermoelasticity with second sound – A review,” Appl. Mech. Rev., vol. 39, no. 3, pp. 355–376, 1986. DOI: 10.1115/1.3143705.
  • P. Puri, “Plane waves in generalized thermoelasticity,” Int. J. Eng. Sci., vol. 11, no. 7, pp. 735–744, 1973. DOI: 10.1016/0020-7225(73)90003-7.
  • M. Daimaruya and M. Naitoh, “Dispersion and energy dissipation of thermoelastic waves in a plate,” J. Sound Vib., vol. 117, no. 3, pp. 511–518, 1987. DOI: 10.1016/S0022-460X(87)80069-X.
  • K. L. Verma and N. Hasebe, “On the propagation of generalized thermo-elastic vibrations in plates,” Q. J. Polish Acad Sci. Eng. Trans., vol. 47, pp. 299–319, 1999.
  • A. Nayfeh and S. N. Nasser, “Thermoelastic waves in a solid with thermal relaxations,” Acta Mech., vol. 12, no. 1–2, pp. 53–69, 1971. DOI: 10.1007/BF01178389.
  • J. N. Sharma, “Thermoelastic surface waves in a transversely isotropic half-space with thermal relaxations,” Indian J. Pure Appl. Math., vol. 16, pp. 1202–1219, 1985.
  • I. Abubakar, “Free vibrations of a transversely isotropic plate,” Q. J. Mech. Appl. Math., vol. 15, no. 1, pp. 129–136, 1962. DOI: 10.1093/qjmam/15.1.129.
  • F. J. Lockett, “Effect of thermal properties of a solid on the velocity of Rayleigh waves,” J. Mech. Phys. Solids, vol. 7, no. 1, pp. 71–75, 1958. DOI: 10.1016/0022-5096(58)90040-1.
  • R. G. Payton, “Wave propagation in a restricted transversely isotropic elastic solid whose slowness surface contains conical points,” Q. J. Mech. Appl. Math., vol. 45, no. 2, pp. 183–197, 1992. DOI: 10.1093/qjmam/45.2.183.
  • R. Kumar, N. Sharma, P. Lata, and S. M. Abo-Dahab, “Mathematical modelling of Stoneley wave in a transversely isotropic thermoelastic media,” Appl. Appl. Math. Int. J., vol. 12, pp. 319–336, 2017.
  • S. K. Rana and P. K. Sharma, “Application of homotopy perturbation method to study wave propagation in transversely isotropic thermo-elastic three dimensional plate,” Asian J. Adv. Basic Sci., vol. 1, pp. 30–39, 2013.
  • M. M. Rashidi and S. A. Pour Mohimanian, “Analytic approximate solutions for unsteady boundary layer flow and heat transfer due to a stretching sheet by homotopy analysis method,” Nonlinear Anal. Model. Control, vol. 15, no. 1, pp. 83–95, 2010. DOI: 10.15388/NA.2010.15.1.14366.
  • H. M. Kordkheili, G. G. Amiri, and M. Hosseini, “Axisymmetric wave propagation of thermoelastic transversely isotropic half-space under buried loading using potential functions,” Waves Random Complex Media, vol. 28, no. 4, pp. 760–783, 2018. DOI: 10.1080/17455030.2018.1468120.
  • J. H. He, “Approximate solution of nonlinear differential equations with convolution product nonlinearities,” Comput. Methods Appl. Mech. Eng., vol. 167, no. 1-2, pp. 69–73, 1998. DOI: 10.1016/S0045-7825(98)00109-1.
  • J. H. He, “Homotopy perturbation technique,” Comput. Methods Appl. Mech. Eng., vol. 178, no. 3-4, pp. 257–262, 1999. DOI: 10.1016/S0045-7825(99)00018-3.
  • S. J. Liao, “On the homotopy analysis method for nonlinear problems,” Appl. Math. Comput., vol. 147, no. 2, pp. 499–513, 2004. DOI: 10.1016/S0096-3003(02)00790-7.
  • M. Jalaal, D. D. Ganji, and F. Mohammadi, “He’s homotopy perturbation method for two-dimensional heat conduction equation,” Heat Transf. Asian Res., vol. 39, no. 4, pp. 232–245, 2010. DOI: 10.1002/htj.20292.
  • A. A. Kilany, S. M. Abo-Dahab, A. M. Abd-Alla, and A. N. Abd-alla, “Photothermal and void effect of a semiconductor rotational medium based on Lord-Shulman theory,” Mech. Based Des. Struct. Mach. DOI: 10.1080/15397734.2020.1780926.
  • S. M. Abo-Dahab, A. M. Abd-Alla, and A. A. Kilany, “Electromagnetic field in fiber reinforced micropolar thermoelastic medium using four models,” J. Ocean Eng. Sci., vol. 5, no. 3, pp. 230–248, 2020. DOI: 10.1016/j.joes.2019.12.003.
  • S. M. Abo-Dahab, S. Z. Rida, R. A. Mohamed, and A. A. Kilany, “Rotation, initial stress, gravity and electromagnetic field effect on P wave reflection from stress-free surface elastic half-space with voids under three thermoelastic models,” J. Mech. Mech. Eng., vol. 22, no. 1, pp. 313–328, 2018. DOI: 10.2478/mme-2018-0027.
  • A. M. Abd-Alla, S. M. Abo-Dahab, and A. A. Kilany, “Effect of several fields on a generalized thermoelastic medium with voids in the context of Lord-Shulman or dual-phase-lag models,” Mech. Based Des. Struct. Mach. DOI: 10.1080/15397734.2020.1823852.
  • F. S. Bayones, A. A. Kilany, A. E. Abouelregal, and S. M. Abo-Dahabd, “A rotational gravitational stressed and voids effect on an electromagnetic photothermal semiconductor medium under three models of thermoelasticity,” Mech. Based Des. Struct. Mach., pp. 1–27, 2021. DOI: 10.1080/15397734.2020.1863229.
  • J. Bouslimi, M. Omri, A. A. Kilany, S. M. Abo-Dahab, and A. Hatem, “Mathematical model on a photothermal and voids in a semiconductor medium in the context of Lord-Shulman theory,” Waves Random Complex Media. DOI: 10.1080/17455030.2021.2010835.
  • E. M. Khalil, S. M. Abo-Dahab, and A. A. Kilany, “Electromagnetic field and initial stress on a photothermal semiconducting voids medium under thermoelasticity theories,” Math. Methods Appl. Sci., vol. 44, no. 9, pp. 7778–7798, 2021. DOI: 10.1002/mma.6942.
  • S. M. Abo-Dahab, A. A. Kilany, E. A.-B. Abdel-Salam, and A. Hatem, “Fractional derivative order analysis and temperature-dependent properties on p- and SV-waves reflection under initial stress and three-phase-lag model,” Results Phys., vol. 18, pp. 103270, 2020. DOI: 10.1016/j.rinp.2020.103270.
  • A. M. Abd-Alla, S. M. Abo-Dahab, and A. A. Kilany, “Finite difference technique to solve a problem of generalized thermoelasticity on an annular cylinder under the effect of rotation,” Numer. Methods Partial Diff. Eq. vol. 37, no. 3, pp. 2634–2646, 2021. DOI: 10.1002/num.22753.
  • F. S. Bayones, S. M. Abo-Dahab, A. M. Abd-Alla, S. H. Elhag, A. A. Kilany, and M. Elsagheer, “Initial stress and gravity on P-wave reflection from electromagneto-thermo-microstretch medium in the context of three-phase lag model,” Complexity, vol. 2021, Article ID, pp. 1–15, 2021. DOI: 10.1155/2021/5560900.
  • F. S. Bayones, A. A. Kilany, S. M. Abo-Dahab, and A. M. Abd-Alla, “Electromagnentic filed and rotation for fractional derivative order calculus with temperature-dependent on reflection of longitudinal wave under initial stress and three-phase-lag model,” Waves Random Complex Media, pp. 1–21, 2022. DOI: 10.1080/17455030.2022.2036385.
  • M. Ragab, S. M. Abo-Dahab, A. E. Abouelregal, and A. A. Kilany, “A thermoelastic piezoelectric fixed rod exposed to an axial moving heat source via a dual-phase-lag model,” Complexity, vol. 2021, pp. 1–11, 2021. 11 pages . DOI: 10.1155/2021/5547566.
  • S. M. Abo-Dahab, “Electromagnetic field and rotational effects on S-waves propagation in a non-homogeneous anisotropic incompressible medium under initial stress and gravity field,” Appl. Math. Inf. Sci., vol. 10, no. 1, pp. 363–376, 2016. DOI: 10.18576/amis/100139.
  • S. M. Abo-Dahab, “Generalized thermoelasticity with diffusion and voids under rotation, gravity and electromagnetic field in the context of four theories,” Appl. Math. Inf. Sci., vol. 13, no. 2, pp. 317–337, 2019. DOI: 10.18576/amis/130221.

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