Hybrid noise control in a duct using a periodic dual Helmholtz resonator array

This paper focuses on the hybrid noise control in a duct using a periodic dual Helmholtz resonator (HR) array. A dual HR which consists of two HRs connected in series (neck-cavity-neck-cavity) leads to two resonance frequencies. A dual HR is analogous to a two degrees of freedom mechanical system. Based on the lumped model, the resonance frequencies and transmission loss of a dual HR have been derived. However, a dual HR is only effective at its resonance peaks with relative narrow bands. Aiming at broader noise attenuation bands for hybrid noise control at low frequencies, a periodic dual HR array is proposed in this paper. The wave propagation in a duct mounted with a periodic dual HR array is investigated theoretically and numerically. The Bragg wave theory and transfer matrix method are developed to conduct the investigation. The predicted theoretical results fit well with the Finite Element Method. Owing to the coupling of Bragg reflection and dual HR's resonances, a periodic dual array can provide much broader noise attenuation bands at the designed resonance frequencies of the dual HR. The proposed periodic dual HR array can be used in practical engineering work to reduce hybrid noise at low frequencies.