Finite Element Modeling of Annular-Like Acoustic Cavities

A finite element technique has been developed to find natural frequencies and modes of undamped three-dimensional acoustic cavities. This method utilizes the analogy between a special form of the discretized transient heat conduction equations and discretized equations of acoustic pressure oscillation. The proposed technique is verified by applying it to several cavities of known theoretical eigen-solutions. Computed results for an acoustic ring, an acoustic disk, and a pure annular cavity match extremely well with exact solutions. In addition, the condensation scheme is investigated and guidelines of selecting acoustic master nodes appropriately are also discussed in the paper. Using the validated finite element method along with suitable condensation, the eigenvalue problem of an annular-like cavity is solved. Since the exact solution for this case is not possible, finite element computations for natural frequencies and modes are compared with the measured results obtained using an acoustic modal analysis experimental technique; again very good agreement has been found.