Circular concentric Helmholtz resonators

Abstract

The effect of specific cavity dimensions of circular concentric Helmholtz resonators is investigated theoretically, computationally, and experimentally. Three analytical models are employed in this study: (1) A two-dimensional model developed to account for the nonplanar wave propagation in both the neck and the cavity; (2) a one-dimensional solution developed for the limit of small cavity length-to-diameter ratio, l/d, representing a radial propagation in the cavity; and (3) a one-dimensional closed-form solution for configurations with large l/d ratios which considers purely axial wave propagation in the neck and the cavity. For low and high l/d, the resonance frequencies determined from the two-dimensional approach are shown to match the one-dimensional predictions. For cavity volumes with l/d>0.1, the resonance frequencies predicted by combining Ingard’s end correction with one-dimensional axial wave propagation are also shown to agree closely with the results of the two-dimensional model. The results from the analytical methods are then compared with the numerical predictions from a three-dimensional boundary element method and with experiments. Finally, these approaches are employed to determine the wave suppression performance of circular Helmholtz resonators in the frequency domain.