Green function method for nonlinear elastic waves in layered media

We construct the Green function for an elastic medium with a plane source. This Green function is particularly helpful in the analysis of weakly nonli near problems, such as occur in nondestructive acoustic evaluation of bonde d structures. By using a perturbative approach we describe the amplitude di stribution of the second harmonic of the driving frequency by linear equati ons with sources. In deriving the Green function we include both longitudin al and transverse polarizations and consider an arbitrary direction of the wave vector with respect to the layer normal. We show how this Green functi on can be combined with the transfer matrix approach to calculate the field s in layered structures. The examples of second harmonic generation from ha lf space and a single layer are considered. (C) 2001 American Institute of Physics.