FINDING THE EIGENMODES OF 2-DIMENSIONAL CAVITIES WITH 2 AXES OF SYMMETRY

A method for calculating the modes of vibration of two-dimensional cav ities is presented. This method can be used for shapes that are simply connected, having two axes of symmetry. It is based on a method for c omputing wave propagation in waveguides of arbitrarily changing cross section, originally proposed by Roure. The cavity under consideration is approximated by a series of rectangles along one of its axes of sym metry, and treated as a waveguide. The input impedance of this wavegui de is used to calculate the resonant frequencies, and calculation of p ressure along this waveguide shows the corresponding vibrational modes . To demonstrate the validity of the proposed method, we analyze a cir cular cavity, with good agreement to analytical results. We then treat a practical case of a semi-elliptical form used in the cross section of a car mufflers. We also show how this method can be applied to calc ulate the vibrational modes of an ideal membrane.