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Free Gas Pulsation of a Helmholtz Resonator Attached to a Thin Muffler Element
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Abstract
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. In this study, a point impedance method is proposed to solve for the natural frequencies and mode shapes of this combined system. Point impedances are formulated, in analogy to point receptances in structural analysis, from the pressure responses to the volume flow rate inputs at the joint of both Helmholtz resonator and thin muffler element. The frequency characteristic equation is derived and then solved for the natural frequencies and mode shapes. The acoustic four poles are then obtained by substituting the natural frequencies and mode shapes into the general formulations developed by the authors. The results from the analytical method are also compared to the numerical prediction from a three dimensional finite element method.
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Citation
Lai, P. and Soedel, W., "Free Gas Pulsation of a Helmholtz Resonator Attached to a Thin Muffler Element," SAE Technical Paper 980281, 1998, https://doi.org/10.4271/980281.Also In
References
- Ingard U. “On the theory and design of acoustic resonators,” Journal of the Acoustical Society of America 25 6 1037 1061 1953
- Alster M. “Improved calculation of resonator frequencies of Helmholtz resonators,” Journal of Sound and Vibration 24 1 63 85 1972
- Panton R. L. Miller J. M. “Resonator frequencies of cylindrical Helmholtz resonators,” Journal of the Acoustical Society of America 57 6 1533 1535 1975
- Soedel W. Padilla-Navas E. Kotalik B. D. “On Helmholtz Resonator Effects in the Discharge System of a Two Cylinder Compressor,” Journal of Sound and Vibration 30 263 277 1973
- Soedel W. “Gas Pulsations in Compressor and Engine Manifolds,” Short Course Text Book of Purdue Compressor Technology Conference Ray Herrick W. Laboratories, Purdue University 1978
- Tang P. K. Sirignano W. A. “Theory of a generalized Helmholtz resonator,” Journal of Sound and Vibration 26 2 247 262 1973
- Selamet A. Dickey N. S. Radavich P. M. Novak J. M. “Theoretical, computational and experimental investigation of Helmholtz resonators: one-dimensional versus multi-dimensional approach,” SAE 940612 1994
- Selamet A. Dickey N. S. Novak J. M. “Theoretical, Computational, and Experimental Investigation of Helmholtz Resonators with Fixed Volume: Lumped versus Distributed Analysis” Journal of Sound and Vibration 187 358 367 1995
- Selamet A. Radavich P. M. “Helmholtz resonator: a multidimensional analytical, computational, and experimental study,” SAE 951263 1995
- Selamet A. Radavich P. M. “Circular concentric Helmholtz resonators,” Journal of Acoustical Society of America 101 1 41 51 1997
- Lai P. C.-C. Soedel W. “Two Dimensional Analysis of Thin, Shell or Plate Like Muffler Elements,” Journal of Sound and Vibration 194 2 137 171 1996
- Lai P. C.-C. Soedel W. “Two Dimensional Analysis of Thin, Shell or Plate Like Muffler Elements of Nonuniform Thickness,” Journal of Sound and Vibration 195 3 445 475 1996
- Kim J. “Simulation of High Speed Hermetic Compressor with Special Attention to Gas Pulsation in Three-Dimensional Continuous Cavities,” Purdue University 1988
- Kim J. Soedel W. “Development of a General Procedure to Formulate Four Pole Parameters by Modal Expansion and Its Application to Three-Dimensional Cavities,” ASME Journal of Vibrations and Acoustics 112 452 459 1990
- Lai P. C.-C. Soedel W. “Free Gas Pulsations in Acoustic Systems Composed of Two Thin, Curved or Flat, Two-Dimensional Gas Cavities Which Share a Common Open Boundary,” Journal of Sound and Vibration 198 225 248 1996
- Kinsler L. Frey A. Coppens A. Sanders J. “Fundamentals of Acoustics,” John Wiley third New York 1982
- Munjal M. L. “Acoustics of Ducts and Mufflers with Application to Exhaust and Ventilation Design,” Wiley-Interscience New York 1987
- Pierce A. D. “Acoustics: An Introduction to its Physical Principles and Applications,” The Acoustical Society of America second 1991
- Morse P. M. “Vibration and Sound,” The Acoustical Society of America second 1991
- Hoffman J. D. “Numerical Methods for Engineers and Scientists,” McGraw-Hill New York 1992
- “ANSYS User's Manual,” Houston, PA 1995