NOISE CONTROL IN DUCTS USING PERIODIC HELMHOLTZ RESONATORS
Brenno Victor Lima Campos1; Audrey Babinet1; José Maria Campos dos Santos1
1 State University of Campinas - UNICAMP
doi:10.20906/CPS/CILAMCE2017-0425
Resumo
Helmholtz resonators have been used extensively in acoustic engineering as passive devices to reduce noise in narrow frequency bands. In the last decades, some approaches have been proposed to improve the performance of Helmholtz resonator. Many of them concentrate on tuning the resonance frequency to enlarge the resonance bandwidth and improve the transmission loss. To broaden the frequency bandwidth, configurations of Helmhlotz resonator in array are proposed. An interesting and promising approach to obtain a broader attenuation range in a duct consists in to distribute local resonators branch-side type with Helmholtz resonators periodically along the duct. This generates some frequency bands, known as "stop bands" or "band gaps", were harmonic waves do not propagate. Bandgaps commonly studied in the area of phononic crystals and metamaterials are generated based on the spatial frequency of mismatched impedance areas which produce Bragg scattering effect and local resonance effect from the Helmholtz resonators. This work investigates the band gaps created in duct-resonator system using acoustic transfer matrix method (TMM), finite element models (FEM) and wave finite element (WFE) models. Periodic geometry variations are investigated. The Floquet-Bloch theorem is used on a transfer matrix of the periodic cell rearranged from an acoustic dynamic stiffness matrix to obtain the dispersion diagrams that reveal the band gaps caused by Bragg scattering and local resonance. Numerical predictions of the forced response obtained with the full FEM model of a duct-resonators system with five cells are compared with a TMM and WFE model.
Palavras-chave: bandgaps; helmholtz resonator; duct; noise control