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Helmholtz resonator has been used in industry for a long time to reduce the noise from exhaust system in vehicle or machinery. Numerous investigations have been done in the past to study the effect of a Helmholtz resonator connected to a pipeline. A general procedure for the analysis of curved or flat, thin two dimensional gas cavities such as thin compressor or engine manifolds or so-called thin shell type muffler elements, which can efficiently utilize the limited space of hermetically sealed compressors or small engine compartments, has been developed by the authors, as long as the thickness of the cavities is substantially small compared to the shortest wavelength of interest. However, to the authors' knowledge, a Helmholtz resonator attached to a rectangular thin muffler element, which is similar to a refrigeration compressor muffler, has not been analyzed.

A general procedure for the analysis of curved or flat, thin two dimensional muffler elements, which can efficiently utilize the limited space of hermetically sealed compressors or small engine compartments, was developed. This procedure can also be applied to analyze thin compressor or engine manifolds as long as the thickness of the cavities is sufficiently small compared to the shortest wavelength of interest. The two dimensional inhomogeneous wave equation, which takes nonuniform thickness into account, is expressed in two dimensional curvilinear coordinates by the application of Hamilton's principle. Four pole parameters are formulated from the pressure response solutions using the modal series expansion method and orthogonality property. A practical four-cylinder automotive compressor was analyzed as an application example. The pressure response at the discharge port excited by input refrigerant was obtained by this general procedure.