Transient response of a layered elastic half space subjected to a reciprocating anti-plane shear load

The well-known Cagniard's technique seems very useful for analyzing the transient problem of an elastic body subjected to a moving load with uniform velocity, but, in the cases of non-uniform velocity it would be difficult to apply the technique directly to analyze the problem. For such cases, instead of the technique, the convolution theorem of the Laplace transform or the dynamic Betti-Rayleigh reciprocal theorem has been applied usefully by many authors.In this paper, an inversion scheme which enables us to apply the Cagniard's technique directly to those difficult problems is presented by solving the problem of a reciprocating anti-plane shear load applied to a layered elastic half space. In this treatment it will be found clearly that our technique is simpler and more systematic than any other techniques for solving the problem. Numerical results are shown in the form of curves and the wave-front singularities are also investigated.