Modeling of acoustic resonators and resonator arrays with non-ideal geometries

Acoustic resonators offer stable, cost-effective attenuation for many noise control applications. Due to their widespread use in engineering and physics, analytical expressions with varying degrees of accuracy have been obtained to predict performance. However, most of the existing formulations are limited to ideal geometries with sharp transitions between two regions. Practical applications of these acoustic resonators often involve space limitations that necessitate curved segments and gradual transitions. This research aims to better characterize the response of non-ideal geometry acoustic resonators. Using currently available expressions for duct bends, the acoustic impedance of bends with various angles and lengths is determined, in an effort to develop relatively simple models for incorporating such elements in a resonator. Other non-ideal geometries as they relate to Helmholtz resonators and arrays of resonators are also explored. These calculations are compared to experimental impedance measurements for validation of the model.