Interior near-field acoustic holography based on finite elements

This paper deals with the mathematical framework of near-field acoustic holography based on finite elements in application to the acoustic response of a fluid within a closed cavity to the enclosure boundary conditions. The finite element method is an effective implementation of the modal approach for arbitrary geometries and provides advantages for certain wavenumber intervals in rooms. An inverse implementation of the direct problem can benefit from using generalized coordinates with modally reduced system matrices. A solution can be obtained via singular value decomposition together with Tikhonov regularization. This paper investigates acoustic mode spectrums of acoustic transfer functions, which has a major effect on the reconstruction of particle velocities from given sound pressures in a simple cavity model. It is found that the largest considered modal wavenumber in the acoustic transfer matrix should be twice the maximum excitation wavenumber. Furthermore, the relation between reconstruction errors and the detectability of evanescent waves depending on the wavenumber of excitation is considered. The proposed method is validated experimentally by reconstructing particle velocities on the inner boundaries of an Airbus A400M fuselage based on measurements of the inner pressure field. Results are compared with structural velocities measured with a laser Doppler vibrometer.