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

Abstract

The basis for the derivation of elastodynamic holography for arbitrarily oriented transversely isotropic materials, given in Part I of this presentation [M. Spies, J. Acoust. Soc. Am. 96, 1144–1157 (1994)], is Huygens’ principle and a resulting relationship which links the spatial spectra of surface traction and displacement distribution. Similar to deriving the plane-wave spectral decomposition of elastic wavefields for given 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 reasonable distribution of surface traction within the transducer aperture, an integral representation for the resulting transducer field is obtained. The main problem in this approach is the inversion of the 2-D space-time spectral representation of Green’s triadic function. A specifically interesting result of this inversion is the Rayleigh function for arbitrarily oriented transversely isotropic media, which characterizes the propagation of the respective Rayleigh wavefronts. Since the resulting expressions are explicitly dependent on the orientation of the material’s axis of rotational symmetry, their numerical evaluation will be much more complicated than in the isotropic case.