Reflection of Elastic Waves from Plane Surface of a Half-space with Impedance Boundary Conditions

Abstract

In the present work, a problem on the reflection of elastic waves at a plane surface of an elastic half-space is considered. The elastic half-space is assumed homogeneous and isotropic. The plane surface of half-space is subjected to impedance boundary conditions, where normal and tangential tractions are proportional to normal and tangential displacement times frequency, respectively. The reflection coefficients of reflected P and SV are obtained in closed form for incidence of P or SV waves. These reflection coefficients depend on the angle of incidence, impedance parameters and other material parameters. The material parameters of Diabase (dark-colored igneous rock), Limestone (sedimentary rock) and Gneiss (high grade metamorphic rock) are chosen to compute the reflection coefficients for certain ranges of angle of incidence and impedance parameters. The effect of impedance boundary on the reflection phenomena is shown graphically for three different rock materials (Diabase, Limestone and Gneiss).

Influence of Diffusion and Impedence Parameters on Wave Propagation in Thermoelastic Medium

“…Vinh and Hue [19] studied propagation of Rayleigh waves in an incompressible elastic half-space having impedence boundary conditions. Singh [20] investigated the problem of the reflection of elastic waves at a plane surface of an elastic half-space subjected to impedence boundary conditions.…”

Reflection and Propagation of Magneto-Thermoelastic Plane Waves at Free Surfaces of a Rotating Micropolar Fibre-Reinforced Medium under G-L Theory

“…17 Singh studied reflection of elastic plane surface waves with impedance boundary conditions. 18 Surface waves in a fibre-reinforced media were considered by Sengupta and Nath. 19 Chattopadhyay, Venkateswarlu, and Saha investigated wave reflection in fibre-reinforced medium with free and rigid boundaries.…”

Three‐dimensional problem of Rayleigh waves propagating in a half‐space with restrained boundary

“…The study of free waves in a half-space (waves propagating with amplitudes determined by accuracy of arbitrary amplitude factor) for classical-traditional and auxetic-non-traditional materials is carried out in [18][19][20][21][22][23][24][25]. The propagation of Rayleigh waves in isotropic elastic semi-space (plane deformation) with impedance boundary conditions (on the semi-space boundary normal and tangential stresses are linear in corresponding displacement component multiplied by the frequency) are studied in [28][29][30][31][32]. The existence and uniqueness of the wave is proved and an analytical formula for the Rayleigh wave speed is obtained using the method of complex functions.…”

“…From mathematical viewpoint, the derivation of the characteristic equation for the Rayleigh wave speed is a eigenvalue problem. In the case of impedance boundary conditions, [28][29][30][31][32] the eigenvalue also enters into the boundary conditions. Such eigenvalue problems are thoroughly studied in [33].…”