Prediction of flow induced sound and vibration of periodically stiffened plates

Stiffened structures excited by the turbulent boundary layer (TBL) occur very frequently in engineering applications; for instance, in the wings of airplanes or the pressure hulls of submarines. To improve knowledge of the interaction between stiffened structures and TBL, this paper deals with the modeling of infinite periodically stiffened plates excited by TBL. The mathematical formulation of the problem is well-established in the literature. The originality of the present work relies on the use of a wavenumber-point reciprocity technique for evaluating the response of the plate to convected harmonic pressure waves. It follows a methodology for estimating the vibro-acoustic response of the plate excited by the TBL from the wall pressure spectrum and its displacements in the wavenumber space due to point excitations located at the receiving positions. The computing process can be reduced to the numerical integration of an analytical expression in the case of a periodically stiffened plate. An application to a naval test case highlights the effect of Bloch-Floquet waves on the vibrations of the plate and its radiated pressure in the fluid.