Modeling systems of acoustic resonators for application in passive noise control

Acoustic resonators, such as Helmholtz and quarter wave resonators, are commonly used as narrowband attenuators in small enclosures. The widespread use of resonators has led to many analytical expressions and approximations for their response, especially for the ideal geometry case. While these resonators are limited in bandwidth, systems of resonators can be designed to obtain responses not otherwise attainable by a single element. Additionally, practical applications of these systems often require non-ideal geometries to be implemented in the design process. This research aims to incorporate equivalent circuit techniques to more accurately characterize the input impedance of a system of resonators. Using the calculated input impedance of the system, an optimal coupling location is determined using a model of the coupled source and enclosure. These calculations are compared to experimental results for validation.