Improved integro-modal approach with pressure distribution assessment and the use of overlapped cavities

An integro-modal approach was previously developed in order to compute the normal modes of an acoustic enclosure of any shape. Though good approximation was achieved for estimating the natural frequencies, we show in this paper that improvement is still needed to ensure good pressure gradient continuity, which is crucial for the convergence of the numerical expression of the pressure distribution into the whole cavity. The technique of overlapped cavities is introduced in the general eigenvalue equations derived from the integro-modal theory. Numerical tests are performed to assess both the original and the modified approach, with special focus on the pressure approximation. The agreement between theoretical or other existing results and numerical solutions using the new approach is improved, in comparison to the results observed with the original approach.