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Calculation of the Transition Matrix for the Scattering of Acoustic Waves from a Thin Elastic Spherical Shell Using the COMSOL Multiphysics Finite-Element Code

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Master's thesis

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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 ka1 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.

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  • Acoustics

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