Inverse problem regularization for the vibroacoustic transfer function construction [French]

摘要

Numerical building of the vibroacoustic transfer function for a structure vibrating in its real environment needs to proceed to the vibroacoustic inverse problem resolution from measured acoustic pressures. These pressures allow actually a density function allocated to point sources on the structure to be calculated. Thus, the obtained function values, coupled with vibratory velocities measured at the same point sources, constitute the data in order to determine the vibroacoustic transfer function. This latter permits the acoustic radiation from the structure on its site to be predicted for any new vibratory state. Our paper presents first and in a short manner, the mathematical formulation establishing the vibroacoustic transfer function construction. Next, the numerical resolution of the inverse problem is detailed. This is typically an ill-posed problem, introduced by a Fredholm integral equation of the first kind. The inversion is carried out with SVD. The regularization process is based on the Miller method using a priori information on the solution and on the measurement errors contaminating the acoustic data. Some numerical simulations and experimental results illustrate the presentation of this regularization test. [References: 31]