Calculation of the transition matrix for the scattering of acoustic waves from a thin elastic spherical shell using the COMSOL Multiphysics Finite-Element Code

摘要

In acoustics, the so-called Transition, or T-matrix relates the incident and scattered acoustic pressures of an object or scatterer. The T-matrix of a thin steel spherical shell in water has been determined by the COMSOL Multiphysics Finite-Element Code. The shell has an outer radius of 0.5m and a thickness of 1cm. It is driven at a frequency of 474 Hz such that ka=1 (where k is the acoustic wave number and a is the outer radius of the shell). A standing wave, represented by a spherical Bessel function, is incident onto the shell surface and the corresponding scattering coefficient is computed. The approach is divided into three portions. Firstly, a fluid-loaded rigid sphere is modeled using the Acoustic-Shell Interaction (ACSH) physics mode to examine the functionality of COMSOL. It also explores the degree of improvement when a refined fluid mesh is applied. Secondly, a thin spherical shell is modeled in the ACSH physics mode. This will examine the credibility of COMSOL to obtain accurate results based on thin shell approximation. Finally, a true 3D finite element, employing the 3D elastic theory, is created using the Acoustic-Structure Interaction (ACSI) physics mode. The resulting diagonal T-matrix elements achieved an accuracy of 0.1% relative to the analytical T-matrix. Ultimately, these results will be applicable to the modeling of the radiation from an arbitrarily densely-packed array of sonar transducers.