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An analytical solution is presented in this study for the vibro-acoustic analysis of a cavity coupled with a ribbed panel due to an internal point sound source excitation. The solution is validated by comparing the result with that obtained using finite element analysis. Generally good agreements are found between the results. The model is then used to examine the sound transmission either through a single ribbed–panel or multiple ribbed–panels separated by air gaps. Results demonstrate that the rib enhancement is effective to reduce the energy transmission controlled by the panel control modes. Whereas the attenuation of the energy transmission to the panels is more effective for the cavity control modes when multiple ribbed panels with air gaps are used. The result also shows that the depth of the air gaps will also play a part on the sound attenuation across the panel system where a larger air gap will lead to a better sound attenuation.

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This paper presents a new analytical solution for the vibration response of a beam‐stiffened Mindlin plate having a completely free boundary condition by utilizing a finite cosine integral transform. In the solution, the unknown coupling force and moments at the beam/plate interface and the unknown modal constants from the integral transform are determined by the continuity and compatibility conditions at the interface as well as the boundary conditions. It provides an easily implemented tool for exploring complex edge value problems for a class of higher‐order partial differential equations represented by fully free‐stiffened Mindlin thick plates. The validity of the model is evaluated by comparing the calculated free and forced vibration responses of the beam‐stiffened plate with those calculated using a beam‐stiffened thin plate and those from finite element analysis.