IJESM Volume 5, Issue 2 ISSN: 2320-0294 A Quarterly Double-Blind Peer Reviewed Refereed Open Access International e-Journal - Included in the International Serial Directories Indexed & Listed at: Ulrich's Periodicals Directory ©, U.S.A., Open J-Gage, India as well as in ωabell’s Directories of Publishing Opportunities, U.S.A. International Journal of Engineering, Science and Mathematics http://www.ijesm.co.in Page 118 Jun. 16 Effect of imperfect interface on plane wave propagation at micropolar viscoelastic solid/fluid saturated incompressible porous solid Vinod Kaliraman Department of Mathematics, Chaudhary Devi Lal University, Sirsa-125055, India Abstract In this paper, the reflection and transmission of plane waves from imperfect interface separating a micropolar viscoelastic solid half space and a fluid saturated incompressible porous solid half space is studied. A longitudinal wave (P-wave) or transverse wave (SV- wave) impinges obliquely at the interface. Amplitude ratios for various reflected and transmitted waves have been obtained with help of boundary conditions at the interface. 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, imperfect interface as well as on the properties of media. From the present investigation, a special case when fluid saturated porous half space reduces to empty porous solid and micropolar viscoelastic solid half space reduces to micropolar elastic solid has also been deduced and discussed with the help of graphs. Keywords: Micropolar viscoelastic solid, porous, reflection, transmission, longitudinal wave, transverse wave, amplitude ratios, empty porous solid. 1. Introduction Most of natural and man-made materials, including engineering, geological and biological media, possess a microstructure. The ordinary classical theory of elasticity fails to describe the microstructure of the material. To overcome this problem, Suhubi and Eringen (1964), Eringen and Suhubi (1964) developed a theory in which they considered the microstructure of the material and they showed that the motion in a granular structure material is characterized not by a displacement vector but also by a rotation vector. Gautheir (1982) found aluminum- epoxy composite to be a micropolar material. Eringen (1967) developed the linear theory of micropolar viscoelasticity. Many researchers discussed the problems of waves and vibrations in micropolar viscoelastic solids. Based on the work of Fillunger model (1913), Bowen (1980) and de Boer and Ehlers (1990a, 1990b) developed an interesting theory for porous medium having all constituents to be incompressible. Based on this theory, many researchers like de Boer and Liu (1994, 1995), Liu (1999), Singh (2002), de Boer and Didwania (2004), Kumar and Barak (2007), Kumar and Hundal (2007), Kumar et.al. (2011) etc. studied some problems of wave propagation in fluid saturated incompressible porous media. Elastic waves propagation in fluid saturated porous media has its importance in various fields such as soil dynamics, hydrology, seismology, earthquake engineering and geophysics. Imperfect interface considered in this problem means that the stress components are continuous and small displacement field is not. The values of the interface parameters depend upon the material properties of the medium. Recently, using the imperfect conditions at the interface, Chen et.al. (2004), Kumar and Chawala (2010), Kumari (2014)etc studied the various types of wave problems. Using the theory of de Boer and Ehlers (1990) for fluid saturated porous medium and Eringen (1967) for micro polar elastic solid, the reflection and transmission phenomenon of longitudinal and transverse waves at an imperfect interface between micropolar elastic solid half space and fluid saturated porous solid half space is studied. A special case when fluid saturated porous solid half space reduces to empty porous solid half space has been deduced