Transmission and bandgap characteristics of a duct mounted with multiple hybrid Helmholtz resonators

This paper describes a duct mounted with multiple hybrid Helmholtz resonators (HHRs) for low-frequency noise control in a piping system. The newly designed HHR is composed of a cavity and a connective neck with a coupling membrane and a perforated plate. Based on the transfer matrix method and equivalent mass-spring model of the membrane, the acoustic impedance of the HHR can be obtained. Sound radiation performance of the unit cell is carefully investigated using a numerical simulation method. Besides, the transmission loss (TL) and bandgap behavior of finite and infinite pipe can be evaluated, respectively. All the theoretical results are verified with corresponding numerical simulation. It is shown that, compared with traditional HR (THR), the HHR exhibit superior TL performance in the low-frequency region, and the energy radiated through the membrane at the first-order resonant frequency is relatively small. Damping caused by the perforated plate has a considerable impact on both the TL and band structure of the periodic pipe. The underlying physical mechanism is then revealed in combination with acoustic modes in the band structure. Additionally, the effect of the perforated plate on the bandgap coupling characteristics is also examined. Eventually, experimental study is also carried out to validate the acoustic performance of the HHRs. Summarizing, this study provides new insights into noise elimination in periodic piping systems.