Finding the eigenmodes of two-dimensional cavities with two axes of symmetry

ISSN： 1610-1928

Source： Acta Acustica united with Acustica, Vol.82, Iss.6, 1996-11, pp. : 811-822

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Abstract

A method for calculating the modes of vibration of two-dimensional cavities 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 computing 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 symmetry, and treated as a waveguide. The input impedance of this waveguide is used to calculate the resonant frequencies, and calculation of pressure along this waveguide shows the corresponding vibrational modes. To demonstrate the validity of the proposed method, we analyze a circular 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 calculate the vibrational modes of an ideal membrane.