Sound field synthesis on flat panels using a planar source array controlled by its active and reactive radiation modes

Abstract

This work investigates how the active and reactive radiation modes of planar loudspeaker arrays can be used in the synthesis of sound fields generated by plane waves impinging on a rigid flat panel with oblique incidence. Any sound field generated by a source array can be decomposed into its radiation modes, which are related to its radiation efficiencies. The control of multi-channel sources via their radiation modes avoids the overloading of the transducers through the disposal of inefficient modes. The active and reactive radiation modes are, respectively, the eigenvectors of the real and imaginary part of the matrix that couples the sound power of the acoustic model. In this work, the matrix that couples the power is numerically obtained through a finite element analysis of the vibroacoustic problem. The optimal velocities of the loudspeakers membranes are obtained in the least- squares sense from the finite element model and the desired acoustic pressure distribution over the flat panel. Only the most efficient radiation modes are considered, so that a regularized solution is obtained. The impacts of some model parameters in the solution quality are analyzed, such as frequency and the distance between the source array and the rigid panel.