Effect of Rigid Boundary on the Propagation of Torsional Surface Waves in Initially Stressed Gravitating Dry Sandy Medium

Abstract

The paper aims to study, the effect of rigid boundary on the propagation of torsional surface waves in initially stressed gravitating dry sandy half space. The mathematical analysis of the problem has been dealt with the Whittaker function. Assuming the expansion of the Whittaker function up to linear term, it is concluded that the gravity field will always allow torsional waves to propagate. The expansion of the Whittaker function up to quadratic terms shows two such wave fronts may exist in the medium. Finally, it is concluded that the sandy medium without support of a gravity field cannot allow the propagation of torsional surface waves, where as the presence of gravity field always supports the propagation of torsional surface waves regardless of whether the medium is elastic or dry sandy. Numerical results analyzing the velocity equations are discussed and presented graphically. It has been observed that density, rigidities play an important role for the propagation of torsional surface waves. It has been seen that as the non-homogeneity parameter in the layer increases, the velocity of torsional surface wave also increases. It has also been observed that an increase in compressive initial stresses decreases the velocity of torsional surface wave.