Similitude laws for the vibroacoustic response of fluid-loaded plates under a turbulent boundary layer excitation

The theory of similitudes provides simple laws by which the response of one system (usually of small size) can be used to predict the response of another system (usually larger). This paper establishes the exact conditions and laws of similitude for the vibrations and acoustic radiation of a panel immersed in a heavy fluid and excited by a turbulent boundary layer. Previous work on vibroacoustic similitude had not considered the problem of a panel radiating in heavy fluid, for which the radiation impedance of the structure must be scaled. The scaling parameters studied here are the dimensions and thickness of the structure, its material properties, the properties of the acoustic domain, and the convective velocity of the turbulent boundary layer. The corresponding scaling laws are derived analytically and verified numerically; in particular, material properties of scaled panels can be determined with simple geometrical constructions on the diagram of Ashby.