Wave propagation in an anisotropic half-space

Abstract

The surface-wave pulse propagation produced by the normal impact of a sphere on a homogeneous, anisotropic elastic half-space was examined using a closely coordinated theoretical and experimental program of investigation. The anisotropic half-space was modeled by a large Yule marble block which represented a transversely isotropic material; the axis of elastic symmetry was located in the free-surface plane. Analytical expressions were obtained using a combined Laplace-Fourier transform method which provided the formal solution of the three-dimensional Lamb's problem for this study. The derivation was carried out first for general anisotropy; subsequently, the relations of interest were rewritten for the transversely isotropic case. The experiment utilized 3 4 - in. diameter steel spheres which struck the test block at impact velocities of about 20 ft/sec. Semiconductor strain gages and specially fabricated quartz crystal accelerometers were employed to detect the horizontal and vertical components of the disturbance, respectively. The former were mounted both along and normal to radial lines drawn from the impact point in order to detect any quasi-Rayleigh components. The experimental procedure provided surface wave group velocity, group slowness, amplitude and attenuation curves for the Yule marble. The experimental slowness curve was compared to the corresponding analytical phase and group slowness curves computed using both static and dynamic properties of this substance which were determined in this study. A comparison of analytical and experimental data shows much better correlation when the dynamic values of the elastic constants were employed.