Elastic wave propagation in transversely isotropic media. II. The generalized Rayleigh function and an integral representation for the transducer field. Theory

The Basis for the derivation of elastodynamic holography for arbitrarily oriented transversely isotropic materials, given in Part I of thes presenation (M. Spies, J. Acoust. Soc. Am. 96, 1144-1157, 1994) is Huygens'pinciple and a resulting relationship which links the spatial spectra of surface traction and displacement distribution. Similar to deriving the plane-wave spectral decompostion of elastic wavefields for give displacement, this relationship yields a corresponding decomposition for the case of given surface traction which can be applied to model the problem of transducer radiation as significant to nondestructive testing. For a physically resonable distribution of surface traction within the transducer aperture, an integral representation for the resulting transducer field is obtained.