Arch Appl Mech https://doi.org/10.1007/s00419-019-01590-5 Malla Reddy Perati · Sindhuja Ala · Rajitha Gurijala Study of reflection and transmission of axially symmetric body waves incident on a base of semi-infinite poroelastic solid cylinder Received: 12 April 2019 / Accepted: 26 August 2019 © Springer-Verlag GmbH Germany, part of Springer Nature 2019 Abstract This paper deals with the study of the reflection and transmission phenomena when axial symmetric body waves incident on the base of a poroelastic semi-infinite solid cylinder, surrounded by another medium. Cylinder is assumed to be isotropic so that Biot’s theory of poroelasticity can be employed. Reflection and transmission coefficients are computed as a function of angle of incidence in the case of permeable base. In addition, square root of energy ratio is computed for the body waves. Numerical results are presented graphically for two types of poroelastic solids, namely sandstone saturated with kerosene and sandstone saturated with water. Keywords Poroelastic solid cylinder · Reflection · Transmission · Energy ratio · Angle of incidence 1 Introduction The wave reflection and transmission phenomena have long history and received much attention during the past half-century in many scientific fields, such as Marine Seismology, Geotechnical Engineering, Acoustics and Geophysics. Analysis of reflection and transmission phenomena can be used to understand the various materials. Sandstone is a great source for quartz which is very useful in day-to-day life. Sandstone deposits are cylindrical in shape and surrounded by poroelastic medium soil or rock. The study of reflection and transmission of waves incidented at the interface gives the information pertaining to sandstone deposits. The reflection and transmission coefficients are generally based on the medium consisting of two non-homogeneous layers separated by a horizontal interface. In Acoustics, the said coefficients are used to understand the effect of various materials on their acoustic environments. In the research domains such as Geophysics and Medicine, the pertinent analysis can be used as nondestructive evaluation (NDE) tool. Displacement discontinuities conserve energy and yield frequency-dependent reflection and transmission coefficients. To the best of author’s knowledge, some of the contributions in this domain are as follows. Reflection and transmission coefficients for harmonic plane waves incident at arbitrary angles upon a plane linear slip interface are computed in the case of elastic media [1]. Employing transfer matrix method, Bogy and Gracewski [2] derived the plane wave reflection coefficient for a layered solid half-space. In the paper [2], the reflection coefficient is derived for an isotropic, homogeneous elastic layer of arbitrary thickness that is perfectly bonded to such an elastic half- space when plane waves are incident from an inviscid fluid onto the layered solid. Singh [3] discussed the reflection of P - and SV -waves from the free surface of an elastic solid with generalized thermo-diffusion. In the paper [3], it is concluded that the reflection coefficients depend upon the angle of incidence of P- and SV-waves and thermo-diffusion parameters. Amplitude ratios and energy ratios are computed numerically, and the conservation of energy across the interface is verified for an elastic solid half-space [4]. Kumar et al. M. R. Perati · S. Ala · R. Gurijala (B ) Department of Mathematics, Kakatiya University, Warangal, Telangana, India E-mail: rajitha.akshu@gmail.com