Several aspects of three basic problems concerned with the propagation of elastic waves in solid media are explored.Stress and displacement correction terms resulting from application of a subsonically moving point load to the free surface of the infinite half-space are obtained using Fourier transform techniques (the load moves subsonically with respect to the longitudinal and transverse wave speeds). It is shown, for the supersonically travelling point load, that the solution is given, in the limit as the load velocity becomes large, by the well known solution of Sauter for the impulsive point load.Analytic function theory is used to predict the existence of Rayleigh waves on the free surface of the infinite halfspace and Stoneley waves along the welded interface between two dissimilar solid media. A brief analysis shows that free-running waves are also possible on the interior surface of an infinitely long cylindrical cavity. These waves are dispersive, however, because of the introduction of a characteristic length.The early and long time approximations for the hoop stress generated through scattering of a plane dilatational wave by a cylindrical cavity in an infinite medium are developed. Use is made of Friedlandler's Riemann surface representation (early time) and expansion in Fourier series (long time).
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