Mean Flow Effects on a Plate-Backed Cavity. Part 1: Theory

This is part I of a paper dealing with the vibro-acoustic behavior of a baffled plate backed cavity, immersed in a mean flow. The plate is excited by a point force or a plane wave convected by the mean flow. This paper expounds the theory. The formulation is based on a finite element method for both the plate and the cavity. Fluid loading due to mean flow is taken into account through an impedance matrix. This external impedance matrix is calculated using an extended form of the Kirchhoff's integral equation together with a variational boundary element method. To account for the cavity, a system of coupled equations is constructed in terms of structural displacements and acoustic pressure. The solution CPU time is substantially reduced by using a modal expansion in terms of the in vacuo structural modes and rigid cavity modes. Two numerical validation are presented. Part II discusses results regarding the effects of mean flow on the vibro-acoustic indicators of the system.