Exact Geometric Similitude Laws for Flat Plate Vibrations Induced by a Turbulent Boundary Layer

Similitude laws for the vibration response of simply supported plates under random excitations are derived and tested numerically and experimentally for the case of a turbulent boundary layer. Analytical calculations show that under the assumption of proportional sides, perfect similitude in terms of vibration response scaling can be achieved between plates of variable thicknesses. It is also highlighted that even if the similitude conditions are not all satisfied (i.e., a complete scaling of all the involved parameters, from panel dimensions to flow speed), an approximation can be made in the mid-high-frequency domain that leads to satisfactorily scaled results. Based on the analytical study, a series of tests is performed in an anechoic wind tunnel on three-scaled simply supported panels at different flow velocities. Applying the proposed procedure to this set of vibration measurements leads to satisfactory scaling of results between each other.