David J.

We propose the validation of a modal method which uses an (u,phi) formulation with static pressure term and with appropriate static displacement potential by a comparison with different other methods and experiments for the Low-Frequency (LF) vibroacoustic response of a coupled system constituted by an elastic structure containing an internal fluid. The internal fluid can be a light fluid (air) or a dense slightly compressible fluid (water). The approaches used for validating modal approach are: an analytical approach, a Medium-Frequency (MF) numerical approach using a specific algorithm and normally well-adapted to MF analysis of vibroacoustic problems. These approaches are compared to each other and also to a solution coming from a commercial code named 'I-deas/Rayon'. In case of a water-filled cavity, they are also compared to measurements. The modal approach uses different formulations. Among these formulations, the classical (u,p) formulation commonly well-adapted for light fluids like air is replaced by an (u,phi) formulation which takes into account the quasi-uncompressibility of dense fluids like liquids. This latter formulation is the correct formulation because it uses the static displacement potential term. Convergence of the method can be accelerated when using the exact solution of the static displacement potential instead of a classical expression, for the case of a rectangular elastic plate coupled to a parallelepipedic cavity. The comparison between methods was focused on the vibratory response of the plate and the acoustic pressure within cavity in the frequency band [0, 5 000Hz], for both cases of air and water. The vibroacoustic system tested experimentally is a rigid cylindrical box containing a parallelepipedic cavity entirely filled with water which is defined by five infinitely-rigid faces and which is closed at one end by an elastic clamped homogeneous plate. For this system, an analytical solution of the overall vibroacoustic problem can be constructed as a reference solution.