A hybrid modal analysis for enclosed sound fields

A hybrid modal expansion that combines the free field Green's function and a modal expansion will be presented in this paper based on a review and an extension of the existing modal analysis theories for the sound field in enclosures. The enclosed sound field will be separated into the direct field and reverberant field, which have been treated together in the traditional modal analysis. Studies on a point source in rectangular enclosures show that the hybrid modal expansion converges notably faster than the traditional modal expansions, especially in the region near the source, and introduces much smaller errors with a limited number of modes. The hybrid modal expansion can be easily applied to complex sound sources if the free field responses of the sources are known. Damped boundaries are also considered in this paper, and a set of modified modal functions is introduced, which is shown to be suitable for many damped boundary conditions.