Torsional Waves in an Infinite Elastic Solid Containing a Spheroidal Cavity

A low-frequency analysis is presented here for the axisymmetric problem of diffraction of torsional waves by an oblate spheroidal cavity in an isotropic homogeneous elastic medium. The method used gives a complete low-frequency expansion of the scattered field in terms of associated Legendre functions, instead of spheroidal wave functions that one gets by the method of separation of variables. This makes the numerical computation much simpler. Graphs and tables are presented for the displacement distribution on the cavity surface and the nonzero shear stress at the end of the major axis of the spheroid. It is found that for low frequencies and for the values of the ratio (b/a) of the minor and major axes of the spheroid considered here the absolute value of the ratio of the nonzero dynamic and static shear stress evaluated at the end of the major axis is independent of b/a for confocal spheroids. An estimate is also given for the radius of convergence of the low-frequency expansion.