Inverse Characterization of Vibro-Acoustic Subsystems for Impedance-Based Substructuring Approaches

Substructuring approaches are helpful methods to solve and understand vibro-acoustic problems involving systems as complex as a vehicle. In that case, the whole system is split into smaller, simpler to solve, subsystems. Substructuring approaches allow mixing different modeling “solvers” (closed form solutions, numerical simulations or experiments). This permits to reach higher frequencies or to solve bigger systems. Finally, one of the most interesting features of substructuring approaches is the possibility to combine numerical and experimental descriptions of subsystems. The latter point is particularly interesting when dealing with subdomains that remain difficult to model with numerical tools (assembly, trim, sandwich panels, porous materials, etc.). The Patch Transfer Functions (PTF) method is one of these substructuring approaches. It condenses information (impedance matrix) of subsystems on their coupling surfaces. In case of a passive subsystem (no source inside), the condensed impedance matrix is the only information needed to couple it to the rest of the system. Classically, this matrix is computed using numerical modeling methods. In the present work, a method to experimentally characterize this impedance matrix is proposed. The main advantage of this method relies on the fact that there is no need to physically uncouple the subsystem to be characterized. Therefore, measurements are only done on the whole system. The theoretical background of this inverse approach will be presented as well as an original way to face ill-posedness of the problem. Finally, a validation on a real acoustic system is proposed.