Scaling laws for flat plate vibroacoustic response induced by deterministic and random excitations

In this paper, some possible applications of scaling-laws for the vibroacoustics of structures are studied. Two experimental works conducted on simply-supported plates submitted to different mechanical and acoustic loadings are described. The first concerns similitudes for the dynamic vibration response and radiated acoustic power of flexural plates under point mechanical excitations. Exact and distorted similitudes and the related scaling laws are investigated from analytical and experimental points of views. All obtained results show that structural response or radiated power of a given plate can be both recovered with satisfactory accuracy by using the related scaling laws, even if parent models are used. The second work concerns similitudes for the vibration of plates under a turbulent boundary layer excitation. Both analytical and experimental analyses are again conducted. It is shown that under the assumption of proportional sides, perfect similitude in terms of vibration response scaling can theoretically be achieved between plates of variable thicknesses. This is experimentally confirmed with the satisfactory scaling of the acceleration autospectral density measured at several discrete points on three parent panels at different flow speeds. The extension of the scaling procedure to cross-spectral density functions is finally studied. As for the autospectral density, the cross-spectral density of acceleration between two points can be effectively retrieved from one panel to another using similitude laws. This opens the possibility of predicting the radiated acoustic power for scaled flow-induced problems, as a bridge between the two summarized works.