Inverse problem regularization for the vibroacoustic transfer function construction

Numerical building of the vibroacoustic transfer function for a structure v ibrating in its real environment needs to proceed to the vibroacoustic inve rse problem resolution from measured acoustic pressures. These pressures al low actually a density function allocated to point sources on the structure to be calculated. Thus, the obtained function values, coupled with vibrato ry velocities measured at the same point sources, constitute the data in or der to determine the vibroacoustic transfer function. This latter permits t he acoustic radiation from the structure on its site to be predicted for an y new vibratory state. Our paper presents first and in a short manner, the mathematical formulation establishing the vibroacoustic transfer function c onstruction. Next, the numerical resolution of the inverse problem is detai led. This is typically an ill-posed problem, introduced by a Fredholm integ ral equation of the first kind. The inversion is carried out with SVD. The regularization process is based on the Miller method using a priori informa tion on the solution and on the measurement errors contaminating the acoust ic data. Some numerical simulations and experimental results illustrate the presentation of this regularization test.