Effects of variable amplitudes of corrugated surface on the dispersion of surface wave on a heterogeneous impedance half-space

Abstract

A Mathematical model analyzing the dispersion of surface waves through the exploration of the theory of elasticity and of a corrugated inhomogeneous fibre-reinforced half-space with heterogeneous impedance conditions at the boundary is investigated. The corrugation is depicted in such a way that the amplitudes of corrugation are dependent on the horizontal coordinate of space and thus, leading to variable amplitudes at the boundary. Using the constitutive equations of fibre-reinforced medium and its governing relations of nonlocal theory of elasticity, the equations of motion were derived. Closed-form solutions of stresses and displacements of the wave on the material are presented by employing the eigenvalue approach otherwise called the normal mode method.  Following this, the analytical and graphical solutions of the results are presented by employing the inhomogeneous impedance and variable corrugation effects at the boundary of the material. We note that the impact of the quantities of nonlocal, wavenumber, variable amplitudes of corrugation, and heterogeneous parameters demonstrates various degree of exhibitions on the dispersion of the Rayleigh wave. One of the parameters associated with variable amplitudes of corrugation cause a downward trend to the dispersion of the Rayleigh wave when its value increases on the solid while its counterpart demonstrate a very clear increase in behavior on the dispersions of the Rayleigh wave in certain domains of the horizontal coordinate or length of the material. The inhomogeneous parameter decreases the dispersion of the Rayleigh wave when its value increase. Thus, we emphasize that this investigation would aid research in geophysics, analysis on surfaces linked to seismology, material designs cum manufacturing, etc.