Wave propagation in transversely isotropic generalized thermoelastic half-space with voids under initial stress Rajneesh Kumar and Rajeev Kumar Department of Mathematics, Kurukshetra University, Kurukshetra, India Abstract Purpose – The purpose of this paper is to study the wave propagation in transversely isotropic generalized thermoelastic half-space with voids under initial stress. Design/methodology/approach – The authors analyze the wave propagation and reflection of plane waves incident at the stress free, thermally insulated or isothermal surface of a homogeneous, transversely isotropic generalized thermoelastic half-space with voids. The graphical representation is given for amplitude ratios of various reflected waves to that of incident waves for different direction of propagation. The phase velocities and attenuation coefficients of plane waves are also computed and presented graphically for various incident angles. Findings – The phase velocities and attenuation coefficients of these plane waves are computed along various direction of wave propagation and the reflection characteristics of these waves, stress free, thermally insulated or isothermal boundary conditions are considered. The amplitude ratios of various reflected waves to that of incident waves have been obtained numerically. Originality/value – Wave propagation in an elastic medium is of great practical importance. Since valuable organic and inorganic deposits beneath the earth surface are difficult to detect by drilling randomly, wave propagation is the simplest and most economic technique and does not require any drilling through the earth. Almost all the oil companies rely on seismic interpretation for selecting the sites for exploratory oil wells because seismic wave methods have higher accuracy, higher resolution and are more economical, compared to drilling, which is expensive and time consuming. The study described in this paper would be very useful for those involved in signal processing, sound system and wireless communication. Keywords Wave propagation, Elasticity, Plane waves, Transversely isotropic, Thermoelastic with voids, Initial stress, Reflection, amplitude ratios Paper type Research paper 1. Introduction The study of dynamic properties of elastic solids is significant in the ultrasonic inspection of materials, vibrations of engineering structures, in seismology, geophysical and various other fields. Such materials are usually described by equations of linear elastic solids; however there are materials of a more complex microstructure (composite materials, granular materials, soils, etc.) depict specific characteristic response to applied load. There are a number of theories which describe mechanical properties of porous materials, and one of them is a Biot consolidation theory of fluid-saturated porous The current issue and full text archive of this journal is available at www.emeraldinsight.com/1573-6105.htm Rajeev Kumar is grateful for the financial support from the Council of Scientific and Industrial Research (CSIR). MMMS 7,4 440 Received 8 April 2011 Revised 5 July 2011 Accepted 12 July 2011 Multidiscipline Modeling in Materials and Structures Vol. 7 No. 4, 2011 pp. 440-468 q Emerald Group Publishing Limited 1573-6105 DOI 10.1108/15736101111185306