The propagation of plane waves in fibre-reinforced, anisotropic, elastic media is discussed. The theory of generalized thermoelasticity proposed by Green and Naghdi is used to solve the problem. Normal mode analysis is used to obtain analytical expressions of the displacement components, stresses, and temperature distribution. Numerical results for the temperature distribution, displacement components, and thermal stress are given and illustrated graphically. Comparisons are made with the results predicted by the Green–Naghdi theory, types II and III, in the presence and absence of fibre-reinforced media.
Similar content being viewed by others
References
A. J. Belfield, T. G. Rogers, and A. J. M. Spence, “Stress in elastic plates reinforced by fiber lying in concentric circles,” J. Mech. Phys. Solids, 31, 25–54 (1983).
S. J. Singh, Comments on “Surface Waves in Fibre-Reinforced Anisotropic Elastic Media” by Sengupta and Nath [Sãdhanã 26 (2001), pp. 363–370], Sãdhanã 27 (2002), pp. 1–3.
Z. Hashin and W. B. Rosen, “The elastic moduli of fiber reinforced materials,” J. Appl. Mech., 31, 223–232 (1964).
H. W. Lord and Y. Shulma, “A Generalized thermodynamical theory of thermoelasticity,” J. Mech. Phys. Solids, 15, 299–309 (1967).
R. Dhaliwal and H. Sherief, “Generalized thermoelasticity for an isotropic media,” J. Quart. Appl. Math., 33, 1–8 (1980).
B. Singh, “Wave propagation in thermally conducting linear fibre-reinforced composite materials,” Arch. Appl. Mech., 75, 513–520 (2006).
P. D. S. Verma, “Magnetoelastic shear waves in self- reinforced bodies,” Int. J. Eng. Sci., 24, No. 7, 1067–1073 (1986).
M. I. A. Othman and I. A. Abba, “Effect of rotation on plane waves at the free surface of a fibre-reinforced thermoelastic half-space using the finite element method,” Meccanica, 46, 413–421 (2011).
A. E. Green and P. M. Naghdi, “A re-examination of the basic postulates of thermomechanics,” Proc. Roy. Soc. London, A432 171–194 (1991).
A. E. Green and P. M. Naghdi, “On undamped heat waves in an elastic solid,” J. Thermal Stresses, 15, 253–264 (1992).
A. E. Green and P. M. Naghdi, “Thermoelasticity without energy dissipation,” J. Elasticity, 31, 189–209 (1993).
M. I. A. Othman and Y. Q. Song, “The effect of rotation on the reflection of magneto-thermoelastic waves under thermoelasticity without energy dissipation,” Acta Mech., 184, 189–204 (2006).
M. I. A. Othman and Y. Q. Song, “Reflection of plane waves from an elastic solid half-space under hydrostatic initial stress without energy dissipation,” Int. J. Solids Struct., 44, 5651–5664 (2007).
M. I. A. Othman, S. Y. Atwa, and R. M. Farouk, “Generalized magnetothermoviscoelastic plane waves under the effect of rotation without energy dissipation,” Int. J. Eng. Sci., 46, 639–653 (2008).
M. I. A. Othman, S. Y. Atwa, and R. M. Farouk, “The effect of diffusion on two-dimensional problem of generalized thermoelasticity with Green-Naghdi theory,” in: Int. Commun. Heat Mass Transfer, 36 (2009), pp. 857–864.
A. J. M. Spencer, Deformation of Fibre-Reinforced Materials, Oxford University Press, London (1972).
Z. Qian, F. Jin, K. Kishimoto, and T. Lu, “Propagation behavior of love waves in a functionally graded half-space with initial stress,” Int. J. Solids Struct., 46, 1354–1361 (2009).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Othman, M.I.A., Atwa, S.Y. Two-dimensional problem of a fibre-reinforced anisotropic thermoelastic medium. Comparison with the Green–Naghdi theory. Comput Math Model 24, 307–325 (2013). https://doi.org/10.1007/s10598-013-9179-9
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10598-013-9179-9