×
Kumar, Rajneesh; Singh, Baljeet

Wave propagation in a micropolar generalized thermoelastic body with stretch. (English) Zbl 0858.73018

Proc. Indian Acad. Sci., Math. Sci. 106, No. 2, 183-199 (1996).
Summary: We discuss two different problems, namely: (i) Rayleigh-Lamb problem in micropolar generalized thermoelastic layer with stretch, and (ii) Rayleigh problem in a micropolar generalized thermoelastic half-space with stretch. The frequency and wave velocity equations for symmetric and anti-symmetric vibrations are obtained for the first problem. The frequency equation has also been derived for the second problem. The special cases of micropolar generalized thermoelasticity with stretch for Green-Lindsay and Lord-Shulman theory have been discussed in detail. Results of these analysis reduce to those without thermal and stretch effects.

Cited in 8 Documents

MSC:

74J10 Bulk waves in solid mechanics
74A35 Polar materials
80A20 Heat and mass transfer, heat flow (MSC2010)

Keywords:

Green-Lindsay theory; wave equation; Rayleigh-Lamb problem; thermoelastic layer; Rayleigh problem; thermoelastic half-space; symmetric and anti-symmetric vibrations; frequency equation; Lord-Shulman theory
Cite Review PDF
Full Text: DOI

References:

[1] Dost, S.; Tabarrok, B., Generalized micropolar thermoelasticity, Int. J. Eng. Sci., 16, 173-183 (1978) · Zbl 0414.73011 · doi:10.1016/0020-7225(78)90046-0
[2] Eringen, A. C.; Suhubi, E. S., Non-linear theory of simple microelastic solids-I, II, Int. J. Eng. Sci., 2, 189-203 (1964) · Zbl 0138.21202 · doi:10.1016/0020-7225(64)90004-7
[3] Eringen, A. C., Micropolar elastic solids with stretch, Ari. Kitabevi Matbassi, 24, 1-18 (1971)
[4] Eringen, A. C., Linear theory of micropolar elasticity, J. Math. Mech., 15, 909-923 (1966) · Zbl 0145.21302
[5] Eringen A C, Foundations of Micropolar Thermoelasticity Course of Lectures No. 23, CISM udine Springer, 1970 · Zbl 0326.73007
[6] Green, A. E.; Lindsay, K. A., Thermoelasticity, J. Elast., 2, 1-1 (1972) · Zbl 0775.73063 · doi:10.1007/BF00045689
[7] Kumar, R.; Gogna, M. L., Propagation of waves in a micropolar elastic layer with stretch immersed in an infinite liquid, Proc. Indian Acad. Sci. (Math. Sci.), 98, 89-99 (1988) · Zbl 0705.73165 · doi:10.1007/BF02880975
[8] Kumar, R.; Chadha, T. K., Lamb’s plane problem in micropolar elastic solids with stretch, Bull. Acad. Pol. Sci., Ser. Sci. Tech., 34, 59-72 (1986) · Zbl 0577.73006
[9] Kumar, R.; Chadha, T. K.; Debnath, L., Lamb’s plane problem in micropolar thermoelastic medium with stretch, Int. J. Math., Math. Sci., 10, 187-198 (1987) · Zbl 0609.73007 · doi:10.1155/S0161171287000723
[10] Lord, H. W.; Shulman, Y., A generalized dynamical theory of thermoelasticity, J. Mech. Phys. Solids, 15, 299-299 (1967) · Zbl 0156.22702 · doi:10.1016/0022-5096(67)90024-5
[11] Müller, I., Arch. Ration. Mech. Anal., 41, 319-319 (1971) · Zbl 0225.73003 · doi:10.1007/BF00281870
[12] Nowacki, W., The plane problem of micropolar thermoelasticity, Arch. Mech. Stosow., 22, 3-3 (1970) · Zbl 0211.28604
[13] Rao, K. M.; Rao, B. K., Propagation of Rayleigh waves in multilayered media, Geophys. Res. Bull., 14, 15-23 (1976)
[14] Sengupta, P. R.; De, S. N., Surface waves in micropolar elastic medium, Bull. Acad. Pol. Sci. Ser., Sci. Tech., 23, 137-146 (1974)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.