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A coupled system consisting of an acoustic cavity and an elastic panel is a classical problem in structural acoustics and is typically analyzed using modal approaches based on in vacuo structural modes and the rigidly walled acoustic modes which are pre-determined based on separate component models. Such modeling techniques, however, tend to suffer the following drawbacks or limitations: (a) a panel is only subjected to ideal boundary conditions such as the simply supported, (b) the coupling between the cavity and panel is considered weak, and (c) the particle velocity cannot be correctly predicted from the pressure gradient on the contacting interface, to name a few. Motivated by removing these restrictions, this paper presents a general method for the vibro-acoustic analysis of a three-dimensional (3D) acoustic cavity bounded by a flexible panel with general elastically restrained boundary conditions. The displacement of the plate and the sound pressure in the cavity are constructed in the forms of standard two-dimensional and 3D Fourier cosine series supplemented by several terms introduced to ensure and accelerate the convergence of the series expansions. The unknown expansions coefficients are treated as the generalized coordinates and determined using the Rayleigh-Ritz procedure based on the energy expressions for the coupled structural acoustic system. The accuracy and effectiveness of the proposed method are demonstrated through numerical examples and comparisons with the results available in the literature.

The vibrations of circular, annular, and sector plates are traditionally considered as different boundary value problems and often treated using different solution algorithms and procedures. This problem is further compounded by the fact that the solution for each type of plate typically needs to be adapted to different boundary conditions. In this paper, a simple solution method is proposed for a unified vibration analysis of annular, circular and sector plates with arbitrary boundary conditions. Regardless of the shapes of the plates and the types of boundary conditions, the displacement solutions are invariably expressed as a new and simple form of trigonometric series expansion with an accelerated convergence rate. The unification of seemingly different boundary value problems for the circular and annular plates and their sector counterparts is physically accomplished by applying a set of coupling springs to ensure appropriate continuity conditions along the radial edges. The accuracy, reliability and versatility of the current method are fully demonstrated and verified through numerical examples involving plates with various shapes and boundary conditions. It should be noted that the current method can be easily applied to sector plates with an arbitrary inclusion angle up to 2 π.