A Generalized Eigenfunction Expansion for Elastodynamics

The use of composite materials in structural components is limited, in part, by the need to develop quantitative inspection techniques. Composites present many challenges to the development of such quantitative methods. For example, composite materials are typically anisotropic. Thus a necessary prerequisite for ultrasonic flaw detection and characterization in composite materials is an understanding of the propagation and scattering of waves in a general anisotropic media. Work towards such an understanding has been typically limited to such issues as beam propagation effects (see, for ex., Ref. [1]). The elastic wave inverse scattering problem (flaw characterization), as well as the simpler direct problem (field-flaw interaction), are only minimally developed for anisotropic media of any kind