Reflection of plane waves at the free surface of a fibre-reinforced elastic half-space

Abstract

The propagation of plane waves in fibre-reinforced, anisotropic, elastic media is discussed. The expressions for the phase velocity of quasi-P (qP ) and quasi-SV (qSV ) waves propagating in a plane containing the reinforcement direction are obtained as functions of the angle between the propagation and reinforcement directions. Closed form expressions for the amplitude ratios for qP and qSV waves reflected at the free surface of a fibre-reinforced, anisotropic, homogeneous, elastic half-space are obtained. These expressions are used to study the variation of amplitude ratios with angle of incidence. It is found that reinforcement has a significant effect on the amplitude ratios and critical angle.

Effect of Rotation and Initial Magnetic Field in Fibre-Reinforced Anisotropic Elastic Media

“…Figure 3 shows that the components of displacement in fibre-reinforced anisotropic elastic media under effect of initial magnetic field, we find that in medium M , the components of displacement 1 u increasing and 2 u decreasing with increasing values of initial magnetic field H respectively, put 1 u′ decreasing and 2 u′ increasing with increasing values of H . Figure 4 shows that the components of stresses in fibre-reinforced anisotropic elastic media under effect of M the components of stresses 11 τ ′ , 22 τ ′ , 33 τ ′ and 12 τ ′ are decreasing with increasing values of Ω . Figure 5 shows that the components of stresses in fibre-reinforced anisotropic elastic media under effect of initial magnetic field, we find in medium M the components of stresses 11 τ , 22 τ Figure 10 shows that the components of displacement in fibre-reinforced isotropic elastic media under effect of rotation, we find in tow medium M and 1 M , all components of displacement are increasing with increasing values of the rotation Ω .…”

“…Figure 4 shows that the components of stresses in fibre-reinforced anisotropic elastic media under effect of M the components of stresses 11 τ ′ , 22 τ ′ , 33 τ ′ and 12 τ ′ are decreasing with increasing values of Ω . Figure 5 shows that the components of stresses in fibre-reinforced anisotropic elastic media under effect of initial magnetic field, we find in medium M the components of stresses 11 τ , 22 τ Figure 10 shows that the components of displacement in fibre-reinforced isotropic elastic media under effect of rotation, we find in tow medium M and 1 M , all components of displacement are increasing with increasing values of the rotation Ω . Figure 11 shows that the components of displacement in fibre-reinforced anisotropic elastic media under effect of initial magnetic field, we find that in the medium M the components of displacement 1 u and 2 u are decreasing and increasing with increasing values of initial magnetic field H , put 1 u′ and 2 u′ are decreasing and increasing with increasing values of H , respectively .…”

“…The elastic moduli for fiber-reinforced materials was given by Hashin and Rosen [21]. The problem of reflection of plane waves at the free surface of a fiber-reinforced elastic half-space was discussed by Singh and Singh [22]. The dispersion of Loves waves in a self-reinforced layer over an elastic non-homogeneous halfspace was studied by Pradhan et al [23].…”

Elastic Waves in a Homogeneous/ an Inhomogeneous Fibre-Reinforced Elastic Half-Spaces

“…The re lection of uasi and uasi S -waves at a plane free and rigid boundaries of a ibre-reinforced elastic medium were investigated (Chattopadhyay et al 2002) and the authors obtained the phase velocity of uasi and uasi S -waves. Singh and Singh (2004) discussed the re lection of plane waves at the free surface of a ibrereinforced elastic half-space and derived the closed form expressions of the amplitude ratios for re lected S and -waves. The scattering of elastic waves from a corrugated interface between two dissimilar ibre-reinforced elastic half-spaces were discussed by Singh and Tomar (2007a) and they obtained the re lection and transmission coef icients with the help of the Rayleigh method of approximation.…”

Shear waves at a corrugated interface between two dissimilar fiber-reinforced elastic half-spaces

“…Pradhan et al [2003] studied the dispersion of Love waves in a self-reinforced layer over an elastic non-homogeneous half-space. Singh and Singh [2004] studied the propagation of plane waves in fiber-reinforced elastic media and showed that the phase velocities of quasi P and SV waves depended on the angle between direction of propagation and the direction of reinforcement. They also discussed the reflection of these elastic waves from the free surface of a fiber reinforced elastic half-space.…”