Reflection-Refraction Coefficients and Energy Ratios in Couple Stress Micropolar Thermoviscous Elastic Solid
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Department of Mathematics, Deenbandhu Chhotu Ram University of Science and Technology, Murthal-, 131039, India
Online publication date: 2021-06-22
Publication date: 2021-06-01
International Journal of Applied Mechanics and Engineering 2021;26(2):47-69
The reflection and refraction phenomenon of propagation of waves in couple stress micropolar thermoviscous elastic solid media with independent viscoelastic and micropolar properties have been studied. The structure of the model has been taken such that the plane interface is divides the given media into two half spaces in perfect contact. Here, we find that there are five waves, one of them is propagating independently while others are set of two coupled waves travelling with different speeds. Energy ratios, reflection and refraction coefficients relative to numerous reflected and refracted waves have been investigated when set of two coupled longitudinal waves and set of two coupled transverse waves strike at the interface through the solid medium. The inequality of energy ratios, refraction coefficients and reflection coefficients are evaluated numerically and presented graphically under three theories of thermoelasticity, namely, Green-Lindsay theory (GL), Lord-Shulman theory (LS), Coupled theory (CT) versus angular frequency and angle of incidence.
Eringen A.C. (1966): Linear theory of micropolar elasticity.– J. of Mech. and Mat. Struct., vol.15, pp.909-923.
Eringen A.C. (1970): Foundations of micropolar thermoelasticity.– Int. J. Eng. Sci., vol.23, Springen-Verlag, Berlin.
Nowacki W. (1986): Theory of asymmetric elasticity.– Oxford, Pergamon.
Dost S. and Taborrok B. (1978): Generalised micropolar thermoelasticity.– Int. J. Eng. Sci., vol.16, pp.173-178.
Green A.E. and Lindsay K.A. (1972): Thermoelasticity.– J. of Elas., vol.2, pp.1-7.
Chandersekharaiah D.S. (1986): Heat flux dependent micropolar thermoelasticity.– Int. J. Eng. Sci., vol.24, pp.1389-1395.
Chandrasekhariah D.S. (1998): Hyperbolic thermoelasticity.– Appl. Mech. Rev., vol.51, pp.705-729.
Farka I.s and Szekers A. (1984): Application of modified law of heat conduction and state equation to dynamical problem of thermoelasticity.– Periodica Poly. Mech. Eng., vol.28, pp.163-170.
Szekers A. (1980): Equation system of thermoelasticity using the modified law of thermal conductivity.– Periodica Poly. Mech. Eng., vol.24, pp.253-261.
Biot A.M. (1965): Mechanics of incremental deformations.– John Wiley and Sons, New York, p.516.
Hetnarski R.B. and Ignaczak J. (1999): Generalised thermoelasticity.– J. of Ther. Str., vol.22, pp.451-476.
Lord H. and Shulman Y. (1967): A generalised dynamical theory of thermoelasticity.– J. of Mech. and Phy. of Solids, vol.15, pp.299-309.
Hetnarski R.B. and Ignaczak J. (1996): Solution like wave in a low temperature nonlinear thermoelastic solid.– Int. J. Eng. Sci., vol.4, pp.1767-1787.
Green A.E. and. Naghdi P.M. (1993): Thermoelasticity without energy dissipation.– J. Elast., vol.31, pp.189-208.
Tomar S.K. and Khurana A. (2008): Transmission of longitudinal wave at plane interface between micropolar elastic and chiral solid half-spaces: incident from micropolar half-spaces.– J. Of Sound and Vib., vol.311, pp. 973-990.
Tomar S. K. and Khurana A. (2017): Waves in non-elastic solids with voids.– Int. J. of Elasticity, vol.128, pp.85-114.
Tomar S. K. and Khurana A. (2018): Waves at the interface of dissimilar nonlocal micropolar elastic half-spaces.– Mech. of ad. Mater. and struct., vol.26, pp.825-833.
Tomar S.K. and Gogna M.L. (1992): Reflection and refraction of longitudinal wave micro-rotational at the interface between two micropolar elastic media in welded contact.– Int. J. Engng. Sci., vol.30, pp.1637-1646.
Tomar S.K. and Gogna M.L. (1995): Reflection and refraction of longitudinal waves at the interface between two micropolar elastic media in welded contact.– J. Acoust. Soc. Am., vol.97, pp.822-830.
Parfitt V.R. and. Eringen A.C. (1969): Reflection of plane waves from the flat boundary of a micropolar elastic half-space.– J. Acoust. Soc. Am., vol.45, pp.1258-1272.
Tomar S.K. (2015): Wave propagation in local and nonlocal microstretch elastic media.– Mec. of ad. Mater. and Struct., vol.84, pp.1-23.
Singh D., Rani N. and Tomar S.K. (2016): Dilatational waves at a microstretch solid/fluid interface.– J. Vibr. Cont., vol.23, pp.3448-3467.
Zhang P., Wei P. and Tang Q. (2015): Reflection of micropolar elastic waves at the non-free surface of a micropolar elastic half-space.– Acta Mech., vol.226, pp.2925-2937.
Zhang P., Wei P. and Tang Q. (2017): Reflection of longitudinal displacement wave at the visco-elastically supported boundary of a micropolar half space.– Meccanica, vol.52, pp.1641-1654.
Achenbach J.D. (1973): Wave propagation in elastic solids.– North Holland, Amsterdam.
Sarkar N. and Tomar S.K. (2019): Plane waves in nonlocal thermoelastic solid with voids.– J. of Thermal Stresses, vol.42, pp.580-606.
Sahrawat R.K., Poonam and Kumar K. (2020): Wave propagation in nonlocal couple stress thermoelastic solid.– AIP Conf. Proceed., vol.2253, pp.1-14.
Poonam, Sahrawat R.K., Kumar K. and Arti (2021): Plane wave propagation in functionally graded isotropic couple stress thermoelastic solid media under initial stress and gravity.– Eur. Phys. J. Plus, vol.136, pp.1-32.
Sahrawat R.K., Poonam and Kumar K. (2021): Plane wave and fundamental solution in non-local couple stress micropolar thermoelastic solid without energy dissipation.– J. of Ther. Stress, vol.44, pp.295-314.
Tomar S.K., Goyal N. and Szekers A. (2019): Plane waves in thermo-viscoelastic material with voids under different theories of thermoelasticity.– Int. J. of Applied Mechanics and Engineering, vol.24, No.3, pp.691-708.
Kumar B., Kumar R. and Kaushal S. (2017): Viscosity effect on reflection and transmission coefficients between two micropolar viscothermoelastic half spaces with three-phase legs.– Int. J. of Eng. Sci. and Res. Tech., vol.9, pp.2348-2369.
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