Effect of Compliant-Diaphragm Geometry on the Transmission Loss Characteristics of Helmholtz Resonators

A classical Helmholtz resonator is commonly used to passively attenuate the tonal noise in ducts. Its drawback is that the attenuation is limited to a single, narrow frequency bandwidth. This work demonstrates that a classical Helmholtz resonator with its one wall replaced by a compliant diaphragm can be used to design a particular transmission loss response and provide a wider bandwidth of attenuation by adjusting the diaphragm dimension. An analytical model is developed for the compliant-wall Helmholtz resonator mounted on a one-dimensional duct and the effect of the diaphragm geometry on the transmission characteristics of the resonator is investigated. The results show that the resonator produces two transmission loss peaks as the diaphragm dimensions meet a certain criteria, beyond which the resonator behaves a similar transmission loss characteristic to that of a classical Helmholtz resonator. Therefore, the wall compliance of the resonator can be neglected so that the wall is taken to be rigid. In addition, the variation tendencies of the transmission loss of the resonator with respect to the diaphragm dimension are discussed. The specific relation between the diaphragm diameter and thickness is given for obtaining a wider attenuation bandwidth.