Browse Publications Technical Papers 2004-01-0387
2004-03-08

Two Degree of Freedom Helmholtz Resonator Analysis 2004-01-0387

The Helmholtz resonator is widely used in vehicle exhaust system tuning. The classic Helmholtz theory is based on the Newton's second law. This approach gives a single resonance frequency and a corresponding attenuation peak.
This paper reviews the approach of the one degree of freedom (DOF) Helmholtz system, and extends it to a two-DOF system. The two-DOF system is composed of two Helmholtz resonators which are in series. The new system is described by a two DOF lump-mass vibration system.
The theoretical derivation of the two-DOF system is presented in this paper. The two-DOF system has two resonance frequencies as expected. The case studies of the two-DOF system are also provided. The developed system has been correlated to computational results (GT-Power©) and experimental results (transmission loss test). The correlation shows that the presented approach for the two-DOF system can correctly predict the resonance frequency of the Helmoltz resonators in general. Due to the limitation of the 1-D model, errors exist in the resonance frequency prediction of complex structures.
The same approach can also be applied to a multiple DOF system. An US patent application has been submitted based upon this design.

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