Free gas pulsations in acoustic systems composed of two thin, curved or flat, two-dimensional gas cavities which share a common open boundary

Abstract A general procedure for the analysis of thin, curved gas cavities has been developed by the authors [1,2], valid for cases where the thickness of the cavity is small compared to the shortest wavelength of interest. Also, the analysis of gas pulsations in multi-cylinder compressor manifolds was demonstrated by the authors [3] as a practical application example. In this study, a line impedance method is proposed for the analysis of composite acoustic systems which consist of two different thin gas cavities which share a common line-like boundary. Line impedances are formulated, in analogy to line receptances in structural analysis, from the pressure responses of thin, curved or flat cavities to a line volume flow rate inputs which are distributed harmonically along the interface of the two subsystems. The composite system frequency equation is derived and then solved for the natural frequencies and mode shapes of the combined acoustic system. Several cases including two rectangular boxes joined together, two cylindrical thin cavities joined together and a circular disk box attached to a cylindrical cavity, which represents a model for a refrigeration compressor manifold, are investigated. Certain results obtained from the line impedance method and finite element method calculations are compared and show satisfactory agreement.