Reconstruction of Interior Sound Fields of Vibrating Shells with an Open Spherical Microphone Array

Abstract

Spherical acoustic holography was utilized to reconstruct the interior sound field of an enclosed space with vibrating boundaries using an open spherical microphone array. The interior sound fields of vibrating shells, including a pulsating shell, a z-axis oriented oscillating shell, a partially vibrating shell and a point-excited vibrating shell, were reconstructed, and numerical simulations were carried out to examine the impact of reconstruction parameters, the radius of the microphone array, the number of microphones, the distribution of microphones on the array surface, the wave number, the number of basis functions used, and the radius of the reconstruction surface on the accuracy of reconstruction. In order to minimize the error of reconstruction caused by a variety of factors and uncertainties, such as the measurement noise, regularization treatments were introduced into the process of reconstructing, to suppress the divergent trends of the reconstruction error along with the increase of the wave number and the increase of the radius of the reconstruction surface. Results showed that a Tikhonov regularization method with generalized cross validation (GCV) could yield the least error of reconstruction among the investigated regularization methods.