An improved mode superposition method applicable to a coupled structural–acoustic system with a multiple cavity

This paper proposes an advanced analytical method that can be used to obtain acoustical modal properties of multiple three-dimensional (3D) cavities, where cavities are connected in series by necks. The method can also be used to obtain the modal properties of a 3D coupled structural–acoustic system including the multiple cavities. The proposed method uses evanescent waves, not considered in previous mode superposition methods, as well as standing waves as basis functions because of discontinuity in the cross-sectional area of a cavity and a neck. Evanescent waves are converted to the added length term of a neck in developing the governing equations. Therefore, the neckʹs effective length, which consists of the physical length and the added length, is used in the characteristic matrix of the governing equation instead of the physical length of the neck. The effective length term increases the exactness of the natural frequencies of the 3D systems of interest and becomes a new control parameter for a coupled system because the evanescent waves can account for the effect of the neckʹs position on multiple cavities. The proposed method is validated by application to one 3D double cavity where two cavities are connected by a neck and three 3D coupled systems including the double cavity. Also, the relative position of the plate and the acoustic pressure distribution of a double cavity are examined for their effect on the degree of coupling.