Acoustically coupled model of an enclosure and a Helmholtz resonator array

This paper presents a general model for dealing with acoustic coupling between an enclosure and a Helmholtz resonator array, which leads to a special model when the array retreats to one resonator. The general model considers a significant number of enclosure modes, resonators, and sources, and gives more accurate prediction results without suffering from the singularity problem met before. The development of the special model results in a rigorous analytical solutions, which allows us to reexamine some of the previous studies reported in literatures. Based on the special model, a frequency equation to predict the frequency variation at both the targeted and off-target modes due to inserting a resonator into the enclosure is provided, and a method to constrain the worsened noise level at off-target modes is also discussed. Comparisons are made among computed data using the present model, previously published models, and measured results, and generally favorable agreement between prediction and measurement is observed. The present model is helpful to numerically evaluate the noise control performance of a resonator array installed in an enclosure, and also useful to semi-analytically determine the optimal location for resonators, which currently still involves heavy experimental measurements on a trial-and-error basis.