Improved integration methods for poles in transfer functions

Abstract

When analyzing stress transmission in layered media as a function of in-plane wave number, the transfer function may exhibit pole-like behavior. These poles are associated with trace matching to bending waves in high stiffness layers. However, the exact interrelationship of multiple poles for the case of multiple various layers is not well understood. This condition presents difficulties to routines that integrate over the wave number. Hence, most users employ adaptive integration schemes that compensate for the poles by increasing the number of points at which the transfer function is evaluated. An improved approach, which involves singularity isolation, is being used in software being developed at BBN. This approach is to describe the pole in an analytical form and perform the integral analytically in the region in which the pole occurs. In this presentation, how to construct the analytic function for a single layer is illustrated, and the generalization to multiple layers is described. This approach leads to a reduction in computer processing time.