Three-dimensional Green’s function approach for analysis of dispersion and attenuation curve in fibre-reinforced heterogeneous viscoelastic layer due to a point source

Abstract

The present paper deals with the propagation of Love waves due to the presence of a point source in the fibre-reinforced heterogeneous viscoelastic medium with the aid of Green’s function technique. The physical parameters, i.e. rigidity and density are assumed to be exponentially and linearly varying function of depth for medium and half-space, respectively. Three-dimensional Green’s function representation for stresses and displacements are derived in complex-plane line-integral. The frequency equations of Love-type waves are derived relating the dependence complex wave numbers after developing the mathematical model with the help of Green’s function and Fourier transformation. This representation is useful in various elastodynamic as well as elastostatic problems. The complex expansion of frequency equation is derived to define the phase velocity and attenuation coefficient of Love waves in the proposed model. Dispersion and attenuation curves are plotted by taking different variations in the reinforcement, inhomogeneity and viscoelastic parameters. The results indicate that the effect of these parameters are very pronounced. The final conclusion can be used to understand the nature of propagation of Love waves in the introduced model.