iPTF methods: How Green's identity and FEM solver can be used for acoustic inverse methods
Résumé
Green's identity is a well-known mathematical tool usually used to solve acoustic problems. If two functions are twice continuously dierentiable, an integral over a volume can be replaced by an integral over the surfaces of this volume. Mostly, one of these functions is the acoustic pressure but the other one is completely arbitrary. The possibilities given by this arbitrary choice are numerous. In the present paper, the powerful capabilities of the Green's identity will be illustrated on a 3D acoustic problem consisting in an oil pan radiating in a semi-innite medium. The radiated eld obtained by Innite Elements (considered here as a reference) will be compared to two solutions provided by the application of the Green's identity on a nite virtual volume surrounding the vibrating surface. Indeed, thanks to Green's identity, the choice of the boundary conditions of this virtual volume is arbitrary. The cases of uniform (Neumann) and mixed (Neumann and Dirichlet) boundary conditions will be presented. Finally, it will be shown how Green's identity and FEM solver can be used as acoustic inverse method. The so-called "uniform iPTF" (inverse Patch Transfer Functions with uniform BC) and "mixed iPTF" (inverse Patch Transfer Functions with mixed BC) will be presented and experimentally applied on the case of the oil pan. Velocity, pressure and intensity elds reconstructed by the inverse methods will be compared to direct measurements.
Domaines
Vibrations [physics.class-ph]
Origine : Fichiers produits par l'(les) auteur(s)
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