Calculation of wave fields using elastodynamic reciprocity

We consider axisymmetric time-harmonic wave motions generated by point-load excitation. Such problems are conventionally solved by the use of integral transform techniques. A typical example is the wave motion generated by a point force in an elastic layer. In this article, it is shown that, in a much simpler manner, the unknown modal coecients for a superposition of wave modes can be conveniently obtained by the use of the Betti±Rayleigh reciprocity theorem. In this integral relation, which connects two elastodynamic states, one of the states is a wave mode of the actual wave ®eld, whereas the other is an appropriately selected auxiliary solution. Simple expressions for the unknown coecients quickly follow. The approach is also applied to the surface wave ®eld generated by a time-harmonic normal point load on a half-space, where the amplitude constant of the generated surface wave motion is obtained