A simple transformation for switching between the stochastic responses in different systems

The progress gained inside the structural and acoustic similitudes makes possible to some extent to change the scales (sizes, materials, topologies, etc.) of many engineering systems. Here, an exact transformation defined by using the Betti theorem, is invoked for the analysis of the stochastic response of the elastic structures wetted by the wall pressure distribution due to a turbulent boundary layer. This kind of response can be severely challenging for both the numerical approaches and the experimental measurement techniques. The transformation, named VOODOO (a versatile offset operator for the discrete observation of objects), is here used for predicting the stochastic responses in two different plates. The method allows connecting the degrees of freedom (in a discrete number of points) of two completely different systems through a matrix operator: if the excitation/response pints are located/evaluated at the points used for building this matrix, the transformation is exact. In the present case, the stochastic pressure loads act on the whole systems and thus the computed responses will be associated to errors: the analysis of these errors is the actual focus.