Attenuation of low-frequency sound in U-shaped duct with membrane coupled acoustic resonator: Modeling and analysis

This study proposes a new solution to control low-frequency noise in acoustic duct. The control device is in the shape of a Helmholtz resonator combined with a tensioned membrane in the air cavity, referred to as a membrane resonator. The membrane resonator is connected to the main waveguide through two necks. A theoretical model is developed to evaluate its acoustic performance when attached to a U-shaped duct as the host structure. Numerical simulation shows that the proposed resonator generates effective transmission loss in the very low-frequency region, as a result of the vibro-acoustic coupling between the integrated membrane and the two-end Helmholtz resonator. Since the attenuation band is deep sub-wavelength, a lumped-mass model is developed to capture the main physics involved in the acoustical-mechanical coupling. With the developed models, the tuning range of the proposed system is further investigated. Several tuning mechanisms are demonstrated by changing the membrane tension, thickness, material type and combining multiple resonators. The transmission loss has fairly large variation range and the desired frequency band is fully controllable. The proposed resonator has simple geometry and mechanical design, whilst the deep sub-wavelength characteristics and the offered tunability are promising. It has the potential to be used solely or as the basic building block in a wide range of noise control applications.