RAY-TRACING OVER SMOOTH ELASTIC SHELLS OF ARBITRARY SHAPE

An efficient numerical scheme based on ray theory is developed for the analysis of elastic waves traveling over a fluid-loaded smooth elasti c shell of arbitrary shape. The shell's surface is first discretized i nto a number of small patches. The local geometry of each patch is the n approximated in a parametric form using bi-cubic spline functions. A local curvilinear coordinate frame is defined on each patch. The ray trajectories and ray-tube areas are obtained by solving a set of ordin ary differential equations, the ray and transport equations, within ea ch patch. Several numerical tests of the accuracy and efficiency of th e scheme were carried out on spherical and ellipsoidal elastic shells: The numerical results for the spherical shell agree well with analyti cal solutions. The ray trajectories and the ray-tube areas over an ell ipsoidal shell with three distinct semiaxes clearly illustrate the inh omogeneous and anisotropic effects due to the variable curvature on th e shell's surface. It is also observed numerically that the magnitude of the ray-tube area along a ray is directly correlated with the stabi lity of its trajectory. (C) 1996 Acoustical Society of America.