On Rayleigh Waves in Self-reinforced Layer Embedded over an Incompressible Half-space with Varying Rigidity and Density

Abstract

In this paper a mathematical model to study the Rayleigh wave propagation in a self-reinforced layer over an incompressible inhomogeneous elastic half-space with quadratically varying rigidity and linearly varying density has been represented. The displacement components for both the media have been deduced separately. Under suitable boundary conditions the secular equation has been established in closed form. Numerical results analyzing the equation are discussed and presented graphically. It is quite ocular that the reinforcement in the upper medium and variations in density and rigidity related to the lower semi-infinite medium has remarkable effect on the Rayleigh wave propagation. Due to the importance of self-reinforced material, the above problem has certain realistic applications in geophysics and civil engineering.