THE DIFFRACTION OF ELASTIC-WAVES BY SPHERICAL DEFECTS

A method of reducing a number of diffraction problems to a system of o ne-dimensional integro-differential equations is proposed based on the method of discontinuous solutions [1, 2] in the case of steady elasti c waves. The defect can be either a spherical crack or a thin rigid sp herical inclusion. The method is described in detail for the second ca se. An effective approximate method of solving the corresponding integ ro-differential equation in the class of functions with non-integrable singularities is proposed in the case of the diffraction of a torsion al wave. A numerical realization of the method is given, namely, graph s of the reactive torsional moment (the inclusion is rigidly fixed) as a function of the oscillation frequency and dimensions of the inclusi on are drawn, and the same graphs for the amplitude of the torsional o scillations of the inclusion when it is mobile (not fixed). (C) 1997 E lsevier Science Ltd.