Variation in the dispersion of axisymmetric waves in infinite circular rods with crystallographic wire texture

This paper presents the solution to the frequency equation for a number of polycrystalline, textured circular rods having transverse isotropy. The eff ective, second-order elastic stiffness tensors were estimated using the rec ursive general Hill arithmetic mean (GHAM). The velocity dispersion curves for a number of combinations of materials and crystallographic fiber or wir e textures were calculated and the variation due to texture displayed. At l arge wavelengths, the velocity dispersion of fiber textured materials exhib its a lowest-order axisymmetric mode which varies only with the directional Poisson's ratios in a manner similar to that of isotropic aggregates. In t his wavelength regime, the waves propagate nondispersively at the wave spee d, C-0, as dictated by the directional Young's modulus. At wavelengths smal ler than the rod radius, the dispersion curves were more influenced by the full anisotropy of the wire textures. At these wavelengths, the dispersion curves for the anisotropic materials deviated significantly from those of t he isotropic materials and one another with the higher axisymmetric vibrati on modes exhibiting extreme differences. This deviation is a function of th e single crystal anisotropy and nature of the wire textures. [S0001-4966(99 )00309-4].