Sensor proximity error in the conformal near-field acoustic holography and its solution by using the nonsingular boundary integral equation

Abstract

In the conformal near-field acoustic holography (NAH) using the boundary element method (BEM), the transfer matrix relating the vibro-acoustic properties of source and field depends solely on the geometrical condition of the problem. This kind of NAH is known to be very powerful in dealing with the sources having irregular boundaries. When the vibro-acoustic source field is reconstructed by using this conformal NAH, one tends to position the sensors as close as possible to the source surface in order to get rich information on the nonpropagating wave components. The conventional acoustic BEM based on the Kirchhoff–Helmholtz integral equation has the singularity problem in the very-near field of the source surface: computation error increases very rapidly as approaching from the far field. This problem originated from the singular kernel of the fundamental solution of the BIE and can influence the reconstruction accuracy. In this paper, the holographic BIE is reformulated to remove the singularity by introducing an additional propagating plane wave. Reconstructed results by the conventional and the nonsingular BIE are compared for a simple radiator model. It is observed that the nonsingular formulation can yield accurate vibro-acoustic transfer matrix and thus improve the resolution of the reconstructed source field.