The effect of a hypocycloid irregularity on torsional surface waves in a multilayer system

The present topic is devoted to investigating the effects of semi four-cusped hypocycloid irregularity on torsional surface waves in an initially stressed anisotropic porous medium situated between two anisotropic non-homogeneous semi-infinite spaces. The irregularity manifests as a semi-four-cusped hypocycloid at the interface where the layer and the lower semi-infinite space are separated. It is assumed that the directional rigidities, density and initial stress vary in the upper and lower semi-infinite spaces in an exponential and hyperbolic manner, respectively. A closed form for the torsional wave dispersion equation is presented. Additionally, the velocity equation is found in the case of no irregularity. The study demonstrates that heterogeneity of lower semi-infinite space, initial stress and directional rigidities of both semi-infinite spaces, as well as of porosity of the layer have a favourable effect on the phase velocity of torsional surface waves. However, the heterogeneity of the upper semi-infinite space, ratio of directional rigidities and initial stress of the layer and irregularity parameter have a negative impact. It has also been observed that, in the case of a uniform media, the velocity equation reduces to the conventional equation for the Love wave.