Hostname: page-component-6bf8c574d5-8gtf8 Total loading time: 0 Render date: 2025-02-21T14:05:38.307Z Has data issue: false hasContentIssue false
  • English
  • Français

Reflection coefficients and energy ratios in a micropolar thermoelastic medium without energy dissipation

Published online by Cambridge University Press:  17 February 2009

Baljeet Singh
Baljeet Singh
Affiliation:
Department of Mathematics, Government College, Sector-11, Chandigarh 160 011, India; e-mail: [email protected].
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The linear governing equations of a micropolar thermoelastic medium without energy dissipation are solved to show the existence of four plane waves in a two-dimensional model. The expressions for velocities of these plane waves are obtained. The boundary conditions at the free surface are used to obtain a system of four nonhomogeneous equations. These equations are solved numerically for a particular model to obtain reflection coefficients for the incidence of coupled longitudinal displacement and coupled transverse microrotational waves. These reflection coefficients as well as the energy ratios are computed and are shown graphically with the angle of incidence in the presence and absence of thermal effects.

Keywords

micropolar thermoelasticityreflection coefficientsenergy ratios.
Type
Research Article
Information
The ANZIAM Journal , Volume 48 , Issue 3 , January 2007 , pp. 433 - 447
Copyright
Copyright © Australian Mathematical Society 2007

References

[1]Abd-Alla, A. N. and Al-Dawy, , “The reflection phenomena of SV waves in a generalized thermoelastic medium”, Int. J. Math. Math. Sci. 23 (2000) 529–546.Google Scholar
[2]Achenbach, J. D., Wave Propagation in Elastic Solids (North Holland, Amsterdam, 1973).Google Scholar
[3]Boschi, E. and Iesan, D., “A generalized theory of linear micropolar thermoelasticity”, Meccanica 8 (1973) 154–157.CrossRefGoogle Scholar
[4]Chandrasekharaiah, D. S., “Thermoelasticity with second sound: A review”, Appl. Mech. Rev. 39 (1986) 355–376.CrossRefGoogle Scholar
[5]Chandrasekharaiah, D. S., “One dimensional waves in thermoelastic half-space without energy dissipation”, Int. J. Engng. Sci. 13 (1996) 1447–1455.Google Scholar
[6]Chandrasekharaiah, D. S., “Thermoelastic plane waves without energy dissipation”, Mech. Res. Commun. 23 (1996) 549–555.Google Scholar
[7]Chandrasekharaiah, D. S., “Complete solutions in the theory of thermoelasticity without energy dissipation”, Mech. Res. Commun. 24 (1997) 625–630.CrossRefGoogle Scholar
[8]Ciarletta, M., “A theory of micropolar thermoelasticity without energy dissipation”, J. Thermal Stresses 22 (1999) 581–594.Google Scholar
[9]Dost, S. and Tabarrok, B., “Generalized micropolar thermoelasticity”, Int. J. Engng. Sci. 16 (1978) 173–183.Google Scholar
[10]Eringen, A. C., Foundations of Micropolar Thermoelasticity, International Centre for Mechanical Science, Courses and Lectures 23 (Springer, Berlin, 1970).Google Scholar
[11]Gauthier, R. D., “Experimental investigation on micropolar media”, in Mechanics of Micropolar Media (eds. Brulin, O. and Hsieh, R. K. T.), (World Scientific, Singapore, 1982).Google Scholar
[12]Green, A. E. and Lindsay, K. A., “Thermoelasticity”, J. Elasticity 2 (1972) 1–7.Google Scholar
[13]Green, A. E. and Naghdi, P. M., “On thermodynamics and the nature of the second law”, Proc. Roy. Soc. London A 357 (1977) 253–270.Google Scholar
[14]Green, A. E. and Naghdi, P. M., “A re-examination of the basic postulates of thermomechanics”, Proc. Roy. Soc. London A 432 (1991) 171–194.Google Scholar
[15]Green, A. E. and Naghdi, P. M., “Thermoelasticity without energy dissipation”, J. Elasticity 31 (1993) 189–209.Google Scholar
[16]Lord, H. W. and Shulman, Y., “A generalized dynamical theory of thermoelasticity”, J. Mech. Phys. Solids 15 (1967) 209–309.Google Scholar
[17]Nowacki, W., Theory of Asymmetric Elasticity (Pergamon, Oxford, 1986).Google Scholar
[18]Parfitt, V. R. and Eringen, A. C., “Reflection of plane waves from a flat boundary of a micropolar elastic half-space”, J. Acoust. Soc. Am. 45 (1969) 1258–1272.CrossRefGoogle Scholar
[19]Singh, B., “Reflection of plane sound wave from a micropolar generalized thermoelastic solid half-space”, J. Sound Vibration 235 (2000) 685–696.Google Scholar
[20]Singh, B. and Kumar, R., “Reflection of plane waves from a flat boundary of a micropolar generalized thermoelastic half-space”, Int. J. Engng. Sci. 36 (1998) 865–890.Google Scholar
[21]Sinha, A. N. and Elsibai, K. A., “Reflection of thermoelastic waves at a solid half-space with two relaxation times”, J. Thermal Stresses 19 (1996) 763–777.CrossRefGoogle Scholar
[22]Sinha, A. N. and Elsibai, K. A., “Reflection and refraction of thermoelastic waves at an interface of two semi-infinite media with two relaxation times”, J. Thermal Stresses 20 (1997) 129–146.Google Scholar
[23]Sinha, A. N. and Sinha, S. B., “Reflection of thermoelastic waves at a solid half-space with thermal relaxation”, J. Phys. Earth 22 (1974) 237–244.Google Scholar