Effect of Gravity and Initial Stress on Torsional Surface Waves in Dry Sandy Medium

Abstract

This problem studies the effect of gravity and initial stress on the propagation of torsional surface waves in dry sandy medium. 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 that 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 a gravity field always supports the propagation of torsional surface waves regardless of whether the medium is elastic or dry sandy.