Non-uniform Helmholtz resonator arrays for broadband sound manipulation

Abstract The use of Helmholtz resonators (HRs) remains a widely adopted approach for passive noise control in ducted systems, particularly at low frequencies. To enhance the bandwidth and efficiency of such treatments, this study examines four HRs array types: single resonators, uniform periodic arrays, non-uniform graded arrays, and periodic non-uniform arrays, to explore their wave manipulation and broadband attenuation capabilities. A single HR demonstrates sharp frequency-selective attenuation, but with a narrow bandwidth. Periodic arrays of identical HRs expand this attenuation range via Bragg scattering and resonant bandgaps, though their performance is limited by symmetry. Non-uniform arrays, where resonators vary in size, enable graded impedance matching and rainbow trapping effects, broadening the attenuation range. Combining periodicity with non-uniform arrays further improves performance by blending the benefits of both approaches. Key factors in optimizing these arrays include resonator coupling, spatial gradients, and the balance between bandwidth and attenuation depth.