Elastodynamic Response of Torsional Waves in Sinusoidal Conical Notch (SCN)

The current study discusses torsional wave transmission in a sandy layer across an orthotropic half-space. The interface that lies between the sandy layer and the half-space is governed by a non-linear function that describes the irregularity of the interface in a certain span along the horizontal axis. The inhomogeneity parameter associated with the media has been governed by a non-linear function as the composition of polynomial, exponential, and cosine functions of depth [Bullen (1940) in Bull. Seismol. Soc. Am. 235–250.].

By means of suitable substitutions and variable-separable techniques, the displacement components have been derived in a closed form. The intrinsic boundary condition at the free surface and the interface have been imposed to deduce the dispersion relation. Two-dimensional graphs have been plotted for phase velocity against radial components to illustrate the influence of inhomogeneity parameters, initial stress, and rigidity ratios.

The phase velocity of the torsional surface wave changes dramatically with respect to the various inhomogeneity parameters. The Biot’s gravity parameter alters the velocity appreciably.