Simplified impedance models for helmholtz resonator with intrusions

This paper presents a simple modeling approach for Helmholtz resonators (HRs) to control low frequency noise in cavities. One of the ways to reduce the natural frequency of a resonator without changing its volume is to introduce an intrusion. Such designs have been studied in detail by other investigators using 3D finite element methods. The focus of this paper is to model single and multiple-orifice intruded HRs using the boundary element (BE) method. Some the models are validated with experimental measurements. From this study it is demonstrated that an intrusion in a single orifice (half the length of the cavity) decreases the lowest natural frequency by about 42 % and the maximum reduction in frequency is obtained for a six orifice HR with 96 mm pitch circle diameter (PCD) of about 56 %. The decrease in frequency is due to a decrease in the reactance (increase in effective mass; increase in inductance) which is demonstrated by calculating the impedance from BE simulations. From the computed impedance values lumped models for intruded resonators is proposed similar to single orifice resonators. Such lumped models will be useful for the design of resonators.