Two Degree of Freedom Helmholtz Resonator Analysis

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.