Reflection and Transmission of Longitudinal Wave at Micropolar Viscoelastic Solid/Fluid Saturated Incompressible Porous Solid Interface

Document Type: Research Paper


Department of Mathematics, Ch. Devi Lal University, Sirsa


In this paper, the reflection and refraction of longitudinal wave from a plane surface separating a micropolar viscoelastic solid half space and a fluid saturated incompressible half space is studied. A longitudinal wave (P-wave) impinges obliquely at the interface. Amplitude ratios for various reflected and transmitted waves have been obtained. Then these amplitude ratios have been computed numerically for a specific model and results thus obtained are shown graphically with angle of incidence of incident wave. It is found that these amplitude ratios depend on angle of incidence of the incident wave as well as on the properties of media. A particular case when longitudinal wave reflects at free surface of micropolar viscoelastic solid has been deduced and discussed. From the present investigation, a special case when fluid saturated porous half space reduces to empty porous solid has also been deduced and discussed with the help of graphs.


[1] Arora A., Tomar S. K., 2010, Seismic reflection from an interface between an elastic solid and a fractured porous medium with partial saturation, Transport in Porous Media 85:375-396.
[2] Bowen R.M., 1980, Incompressible porous media models by use of the theory of mixtures, International Journal of Engineering Science 18:1129-1148.
[3] Chen W., Xia T., Sun M., Zhai C., 2012, Transverse wave at a plane interface between isotropic elastic and unsaturated porous elastic solid half-spaces, Transport in Porous Media 94:417-436.
[4] de Boer R., Didwania A. K., 2004, Two phase flow and capillarity phenomenon in porous solid-a continuum thermomechanical approach, Transport in Porous Media 56:137-170.
[5] de Boer R., Ehlers W., 1990, Uplift, friction and capillarity-three fundamental effects for liquid-saturated porous solids, International Journal of Solids and Structures B 26:43-57.
[6] de Boer R., Ehlers W., 1990, The development of the concept of effective stress, Acta Mechanica A 83: 77-92.
[7] de Boer R., Ehlers W., Liu Z., 1993, One-dimensional transient wave propagation in fluid-saturated incompressible porous media, Archive of Applied Mechanics 63(1):59-72.
[8] de Boer R., LiuZ., 1994, Plane waves in a semi-infinite fluid saturated porous medium, Transport in Porous Media, 16 (2): 147-173.
[9] de Boer R., Liu Z., 1995, Propagation of acceleration waves in incompressible liquid - saturated porous solid, Transport in porous Media 21: 163-173.
[10] de Boer R., Liu Z., 1996, Growth and decay of acceleration waves in incompressible saturated poroelastic solids, Zeitschrift für Angewandte Mathematik und Mechanik 76:341-347.
[11] Eringen A.C., 1967, Linear theory of micropolar viscoelasticity, International Journal of Engineering Science 5:191-204.
[12] EringenA.C., Suhubi E.S., 1964, Nonlinear theory of simple micro-elastic solids I, International Journal of Engineering Science 2:189-203.
[13] Fillunger P., 1913, Der Auftrieb in Talsperren, Osterr, Wochenschrift fur den offen Baudienst, Franz Deuticke,Wien.
[14] Gautheir R.D., 1982, Experimental Investigations on Micropolar Media, Mechanics of Micropolar Media , Brulin O, Hsieh R K T., World Scientific, Singapore.
[15] Gupta V., Vashishth A.K., 2013, Reflection and Transmission Phenomena in Poroelastic Plate Sandwiched between Fluid Half Space and Porous Piezoelectric Half Space, Smart Materials Research.
[16] Kumar M., Saini R., 2012, Reflection and refraction of attenuated waves at boundary of elastic solid and porous solid saturated with two immiscible viscous fluids, Applied Mathematics and Mechanics 33(6): 797-816.
[17] Kumar R., Divya T., Kumar K., 2012, Effect of imperfectness on reflection and transmission coefficients in swelling porous elastic media at an imperfect boundary , Global Journal of Science Frontier Research 12(2) : 88-99.
[18] Kumar R., Hundal B. S., 2007, Surface wave propagation in fluid - saturated incompressible porous medium, Sadhana, 32(3): 155-166.
[19] KumarR., Gogna M.L., Debnath L.,1990, On lamb’s problem in micropolar viscoelastic half-space with stretch, International Journal of Mathematics and Mathematical Sciences 13:363-372.
[20] Kumar R., Miglani A., Kumar S., 2011, Reflection and transmission of plane waves between two different fluid saturated porous half spaces, Bulletin of the Polish Academy of Sciences Technical 59(2):227-234.
[21] Kumar R., Panchal M., 2010, Response of loose bonding on reflection and transmission of elastic waves at interface between elastic solid and micropolar porous cubic crystal, Applied Mathematics and Mechanics 31(5): 605-616.
[22] LiuZ., 1999, Propagation and evolution of wave fronts in two-phase porous media, Transport in Porous Media 34: 209-225.
[23] Parfitt V.R, Eringen A.C., 1969, Reflection of plane waves from the flat boundary of a micropolar elastic half space, Journal of the Acoustical Society of America 45:1258-1272.
[24] Sharma M. D., Kumar M., 2011, Reflection of attenuated waves at the surface of a porous solid saturated with two immiscible viscous fluids, Geophysical Journal International 184: 371-384.
[25] Sharma M. D., Kumar M., 2013, Reflection and transmission of attenuated waves at the boundary between two dissimilar poroelastic solids saturated with two immiscible viscous fluids, Geophysical Prospecting 61(5): 1035-1055.
[26] Singh B., 2000, Reflection and transmission of plane harmonic waves at an interface between liquid and micropolar viscoelastic solid with stretch, Sadhana 25(6):589-600.
[27] Singh B., 2002, Reflection of plane micropolar viscoelastic waves at a loosely bonded solid-solid interface, Sadhana, 27(5):493-506.
[28] Suhubi E.S., Eringen A.C., 1964, Nonlinear theory of micro-elastic solids II, International Journal of Engineering Science 2: 389-404.
[29] Tajuddin M., Hussaini S.J., 2006, Reflection of plane waves at boundaries of a liquid filled poroelastic half-space, Journal of Applied Geophysics 58:59-86.
[30] Tomar S. K., Khurana A., 2011, Transmission of longitudinal wave through micro-porous elastic solid interface, International Journal of Engineering Science and Technology 3(2): 12-21.
[31] Yan Bo., Liu Z., Zhang X., 1999, Finite element analysis of wave propagation in a fluid saturated porous media, Applied Mathematics and Mechanics 20:1331-1341.