A Tunable Helmholtz Resonator for Active Noise Control

Abstract

In this study, a tunable Helmholtz resonator is proposed for active noise cancelation in a primary acoustic system. In the tunable Helmholtz resonator, the resonator’s top wall is replaced by a flexible membrane and four actuators are mounted on the side of the resonator. These actuators are connected to the membrane in order to tune its radial force (tension) by pulling or releasing the membrane during the operation. This causes the resonant frequency of the modified Helmholtz resonator to change due to the change in the membrane tension. The maximum noise attenuation is achieved when the the resonant frequency of the active resonator matches with the noise frequency in the primary system. In this paper, first mathematical modeling is used to derive nonlinear coupled differential equations for the tunable Helmholtz resonator with the membrane. The differential equations were linearized to obtain an analytical formulation for the resonant frequency of the tunable resonator in terms of the membrane tension. The analytical formulation for the resonant frequency was verified via simulation of the original nonlinear differential equations. Finally, to demonstrate the validity of the mathematical modeling of the tunable resonator, experimental results are provided.