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Circular asymmetric Helmholtz resonators

A three-dimensional (3D) analytical approach is developed to account for the nonplanar wave propagation in the cavity and neck of "piston-driven" circular asymmetric Helmholtz resonators. The present 3D analytical results are compared with (1) the numerical predictions from the boundary element method (BEM) to evaluate the analytical approach; and (2) the one-dimensional (1D) solution to examine the effect of nonplanar waves at area discontinuity between the neck and the cavity. In order to improve the 1D solution, the end correction is also determined by using the 3D analytical approach. The effect of neck offset on the resonance frequency of circular asymmetric Helmholtz resonators is investigated. Predictions of resonance frequency and transmission loss from the present 3D and corrected 1D analytical approaches are, respectively, identical and close to the BEM results, while the corrected 1D approach provides a better accuracy compared to the 1D solutions with Ingard's correction. Finally, the boundary element method is employed to determine the wave attenuation performance of the "pipe-mounted" Helmholtz resonators to examine the effect of multidimensional waves in the vicinity of the main duct and neck junction.