Numerical Integration and Angular Spectrum Modeling of Resonant and Non-Resonant Wave Interaction with a Solid Plate

Abstract

The angular spectrum (AS) model is widely used to calculate the pressure transmitted through, and reflected from, a fluid-immersed solid plate, using a baffled piston as source. However, narrow peaks (infinite peaks for the lossless case) in the piston aperture function and in the plane wave transmission and reflection coefficients, in addition to a highly oscillatory integrand, cause challenges in the numerical integration. To overcome the challenges related to the aperture function peak, the AS model is reformulated using integration by parts. The peaks in the transmission and reflection coefficients are identified as symmetric and antisymmetric Scholte modes, and a numerical integration method is provided enabling integration over these peaks. The AS-model is also used to obtain the full-wave diffraction correction for a pulse-train transmitted through, or reflected from, the plate, which is highly relevant in pulse-transmit or pulse-receive measurements. The diffraction effects caused by the plate are calculated by suppressing resonance effects in the plate and obtaining the corresponding plane wave pressure transmission and reflection coefficients. A hybrid Gauss-Filon adaptive numerical integration method is used to calculate the pressure. These calculations are conducted in APAS, a MATLAB program developed in the current work and provided as open-source supplementary material.