Reconstruction of vibro-acoustic fields by using the nearfield acoustical holography based on the nonsingular BEM

Abstract

The nearfield acoustical holography (NAH) based on the boundary element method (BEM) is one of the indirect identification methods for vibro-acoustic source properties. In this method, the sound radiation and transmission between a vibrating source and a hologram plane is modeled by the vibro-acoustic transfer matrix using the boundary integral equation (BIE). Distribution of surface velocities of the source can be reconstructed by multiplying the inverse of the calculated vibro-acoustic transfer matrix and the measured field pressure vector. In principle, the pressure data can be measured at a surface with any shape of the nearfield plane including the conformal one. In this technique, the field pressure should be measured as close to the source as possible in order to acquire precise field information including the non-propagating evanescent waves for an accurate source reconstruction. In three-dimensional problems, a propagating wave in the free field can be a Green function satisfying the Helmholtz equation. In the acoustical BIE, i.e. Kirchhoff-Helmholtz integral equation, monopole and dipole Green functions are proportional to 1/R or 1/$R^2$ when R denotes the distance between source and field point. This means that there is a serious singularity problem in the nearfield. In order to overcome this dilemma, the non-singular boundary integral formulation utilizing propagating plane waves is employed in the NAH. With this kind of BIE, all singularities included in the conventional acoustical BIE can be removed. Consequently, the field pressure can be determined precisely in the very closed field and the acoustical parameters can be continuously calculated on the surface. This can result in the improvement of the BEM-based NAH. Additionally, in applying the BEM-based NAH technique to actual vibro-acoustic problems, it is often possible to measure the surface velocity at some points of the source, directly and easily. Therefore, there is no need to reconstruct...