Similitude laws for the structural response of flat plates under a turbulent boundary layer excitation

Similitude laws for scaling the vibration response of flat panels to a turbulent boundary layer excitation are proposed and analyzed in this paper. Their relevance is studied from an analytical, experimental and numerical perspective. It is first shown that a perfect similitude, in terms of vibration response scaling, can theoretically be achieved between plates of proportional sides and of variable thicknesses. Vibration auto-spectral and cross-spectral density functions, measured in a wind-tunnel facility on a set of three plates, are then successfully scaled: the plates dimensions and test flow speeds are a priori defined using the proposed similitude laws. Finally, the applicability of the suggested strategy for different boundary conditions, for different types of materials and properties and for distorted models is also numerically studied and confirmed.