CIRCULAR CONCENTRIC HELMHOLTZ RESONATORS

The effect of specific cavity dimensions of circular concentric Helmho ltz resonators is investigated theoretically, computationally, and exp erimentally. Three analytical models are employed in this study: (1) A two-dimensional model developed to account for the nonplanar wave pro pagation in both the neck and the cavity; (2) a one-dimensional soluti on developed for the limit of small cavity length-to-diameter ratio, l /d, representing a radial propagation in the cavity; and (3) a one-dim ensional closed-form solution for configurations with large l/d ratios which considers purely axial wave propagation in the neck and the cav ity. For low and high l/d, the resonance frequencies determined from t he two-dimensional approach are shown to match the one-dimensional pre dictions. For cavity volumes with l/d>0.1, the resonance frequencies p redicted by combining Ingard's end correction with one-dimensional axi al wave propagation are also shown to agree closely with the results o f the two-dimensional model. The results from the analytical methods a re then compared with the numerical predictions from a three-dimension al boundary element method and with experiments. Finally, these approa ches are employed to determine the wave suppression performance of cir cular Helmholtz resonators in the frequency domain. (C) 1997 Acoustica l Society of America.