Modeling Acoustic Resonators with Higher-Order Equivalent Circuits

Acoustic resonators such as the Helmholtz resonator find wide use in passive noise control situations. It is well known that classical lumped element formulations for properties of these resonators are inaccurate. Recent work [Calton and Sommerfeldt, Inter-Noise Proc. (2015)] has shown that simple resonators and resonator arrays can be efficiently modeled to high accuracy using impedance translation and junction impedance. This paper will present the continuation of that work to resonators with tapered and curved necks. It will be shown that higher-order calculations of impedance show improved agreement with measured impedance compared to classical formulations. In addition, we will illustrate the application of these improved impedance predictions to transmission loss in a duct with a resonator side branch. A user interface to design resonators according to these higher-order predictions will be demonstrated.