BULK-WAVE POLARIZATION-FIELDS IN TRANSVERSELY ISOTROPIC ELASTIC MEDIA

The bulk-wave polarization field of a transversely isotropic elastic m aterial has three branches, each rotationally symmetric about the axis of transverse isotropy. The branches are not uniquely defined, howeve r, by the propagation condition for plane bulk waves since the polariz ation of each wave is determined only to within a factor of -1. Two gr ound rules are adopted: discontinuities in the branches are restricted to the acoustic axes, along which two or all three of the plane bulk waves have equal speeds; and, in a specified ordering, the three polar izations are taken to form a right-handed orthonormal set. The topolog ical character of the branches depends on the combinations C-11 - C-44 , C-33 - C-44, C-13 + C-44 of the five distinct elastic moduli of the material. In the regular case in which each combination is non-zero, t he ground rules permit an unambiguous specification of the branches, b ut when C-11 = C-44 nonuniqueness results from the presence of discont inuities in the basal plane. Polarization fields are constructed for a ll transversely isotropic elastic materials with positive definite str ain energy and the results are related to an elastodynamic classificat ion of these materials which is similarly exhaustive.