A versatile offset operator for the discrete observation of coupled vibroacoustic systems

There is an increasing attention about structural similitudes, since they allow to change the scales (sizes, materials, topologies, etc.) of any engineering system. Often, the associated predictions are still not fully reliable since the scaling laws can be incomplete and thus it is desired to have methods aimed at defining transformation matrices which link the outputs between two sets of points belonging to different linear systems. The recently defined VOODOO method has demonstrated that a transformation matrix can be defined by using the Betti theorem and it can be invoked for both deterministic and stochastic loads. In principle, with this transformation, two completely different systems can be connected, according to few rules. This paper provides the theoretical framework underlying the extension of VOODOO to the structural-acoustic coupling.