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.

Topics
Helmholtz resonator, Wave propagation, Functional analysis, Boundary element methods, Optical resonators
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1997
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