International Journal of Mathematics Trends and Technology
Volume 55 | Number 6 | Year 2018 | Article Id. IJMTT-V55P553 | DOI : https://doi.org/10.14445/22315373/IJMTT-V55P553
The present investigation deals with the reflection and refraction phenomenon at the imperfect interface between fluid saturated porous solid half space and micropolar elastic solid half space. P-wave or SV-wave is considered to be incident on the plane interface through fluid saturated porous solid half space. Incident wave impinge obliquely at the interface. Amplitudes ratios of various reflected and refracted waves to that of incident wave are derived and deduced for normal force stiffness, transverse force stiffness and for welded contact. After obtaining the amplitudes ratios, they have been computed numerically for a specific model and results obtained graphically with angle of incidence of incident wave. It is found that these amplitude ratios depend on angle of incidence of incident wave and material properties of the medium and these are affected by the stiffness also.
[1] Bowen, R.M., Incompressible porous media models by use of the theory of mixtures, J. Int. J. Engg. Sci. 18, 1129-1148, 1980.
[2] de Boer, and Didwania, A. K., Two phase flow and capillarity phenomenon in porous solid- A Continuum Thermomechanical Approach, Transport in Porous Media (TIPM), 56, 137-170, 2004.
[3] de Boer, R. and Ehlers, W., The development of the concept of effective stress, ActaMechanica A 83, 77-92,1990.
[4] de Boer, R. and. Ehlers, W ,Uplift, friction and capillarity-three fundamental effects for liquid- saturated porous solids, Int. J, Solid Structures B, 26,43-57,1990.
[5] de Boer, R., Ehlers, W. and Liu, Z., One dimensional transient wave propagation in fluid saturated incompressible porous media, Arch. App. Mech. 63, 59-72, 1993.
[6] de Boer, R. and Liu, Z., Plane waves in a semi-infinite fluid saturated porous medium, Transport in Porous Media, 16 (2), 147-173, 1994.
[7] Eringen, A.C. and Suhubi, E.S., Nonlinear theory of simple microelastic solids I, International Journal of Engineering Science,2,189- 203,1964.
[8] Eringen, A.C., Linear theory of micropolar viscoelasticity, International Journal of Engineering Science, 5,191-204, 1968.
[9] Gautheir, R.D., Experimental investigations on micropolar media, Mechanics of micropolar media (eds) O Brulin, R K T Hsieh (World Scientific, Singapore), p.395, 1982.
[10] Kumar, R., Barak, M., Wave propagation in liquid-saturated porous solid with micropolar elastic skelton at boundary surface, Applied Mathematics and Mechanics, 28(3), 337-349, 2007.
[11] Kumar, R. and Hundal, B.S., Wave propagation in a fluid saturated incompressible porous medium, Indian J. Pure and Applied Math.4, 51- 65, 2003.
[12] Kumar, R., Miglani, A. and Kumar, S., Reflection and Transmission of plane waves between two different fluid saturated porous half spaces, Bull. Pol. Ac., Tech., 227-234, 59(2), 2011.
[13] Kumar,R. and Singh,B., Reflection and transmission of elastic waves at a loosely bonded interface between an elastic and micropolar elastic solid, Indian Journal of Pure and Applied Mathematics,28,1133- 1153,1997.
[14] Kumari, N., Reflection and transmission of longitudinal wave at micropolar viscoelastic solid/fluid saturated incompressible porous solid interface, Journal of Solid Mechanics, 6(3), 240-254, 2014.
[15] Kumari, N., Reflection and transmission phenomenon at an imperfect boundary of viscoelastic solid and fluid saturated incompressible porous solid, Bulletin of Mathematics and Statistics Research, 2(3), 306-319, 2014.
[16] Murty, G.S., Reflection, transmission and attenuation of elastic waves at a loosely bonded interface of two half spaces, Geophys. J.R. Astrom. Soc., 44, 389-404, 1976.
[17] Parfitt, V.R, and Eringen, A.C., Reflection of plane waves from the flat boundary of a micropolar elastic half space, J. Acoust. Soc. Am., 45, 1258-1272, 1969. [18] Singh, B. and Kumar, R. Wave reflection at viscoelastic-micropolar elastic interface, Applied Mathematics and Computation ,185,421- 431,2007.
[19] Tomar S. K, and Gogna, M. L., Reflection and refraction of longitudinal microrotational wave at an interface between two different micropolar elastic solids in welded contact, Int. J. Eng. Sci. 30:1637- 1646, 1992.
[20] Tomar, S. K. and Kumar, R., Reflection and refraction of longitudinal displacement wave at a liquid micropolar solid interface, Int. J. Eng. Sci. 33:1507-1515, 1995.
[21] Tajuddin, M. and Hussaini, S.J., Reflection of plane waves at boundaries of a liquid filled poroelastic half-space, J. Applied Geophysics 58, 59-86, 2006.
[22] Vashisth, A.K., and Gogna, M.L., The effect of loose boundaries on wave propagation in a porous solid: reflection and refraction of seismic waves across a plane interface, international Journal of Solid Structure, 30, 2485-2499, 1993.
Vinod Kaliraman, "Effect of Imperfect Interface Between Fluid Saturated Porous Solid and Micropolar Elastic Solid on Wave Propagation," International Journal of Mathematics Trends and Technology (IJMTT), vol. 55, no. 6, pp. 397-405, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V55P553
PDF 
Abstract 
Keywords 
References 
Citation