On a proposed determination of the shear modulus of an isotropic elastic half-space by the forced torsional oscillations of a circular disc

Abstract

It has been suggested that the shear modulus can be determined by the response of an isotropic homogeneous elastic half-space to the forced torsional oscillations of a rigid circular disc attached to its surface. In this paper a series expansion is obtained for the response of an unloaded disc, and the results compared with previous work. A bound is given for the limit of validity of this power series. Consideration is also given to a loaded disc and a range of loading is suggested to give results in keeping with the limits of the expansion. The displacements in the half-space due to the oscillations of an unloaded disc attached to the free surface have also been computed. These vibrational displacements are similar to those caused by a static rotation of the disc. The results are presented in graphical form.