A two-dimensional analytical solution is developed to determine the acoustic performance of a perforated single-pass, concentric cylindrical silencer filled with fibrous material. To account for the wave propagation through absorbing fiber and perforations, the complex characteristic impedance, wave number, and perforation impedance are employed. With expressions for the eigenvalues and eigenfunctions of sound propagation in the perforated dissipative chamber, the transmission loss is obtained by applying a pressure and velocity matching technique. The results from the analytical method are then compared with both experiments and numerical predictions based on the boundary element method ͑BEM͒, showing a reasonable agreement. The effects of geometry, fiber properties, and perforation porosity on the acoustic attenuation performance are discussed in detail.

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A closed-form, two-dimensional analytical solution is developed to investigate the acoustic performance of a concentric circular Helmholtz resonator lined with fibrous material. The effect of density and the thickness of the fibrous material in the cavity is examined on the resonance frequency and the transmission loss. With the expressions for the eigenvalue and eigenfunction in the cavity, the transmission loss is obtained for a piston-driven model by applying a pressure/velocity matching technique. The results from the analytical methods are compared to the numerical predictions from a three-dimensional boundary element method and the experimental data obtained from an impedance tube setup. It is shown that the acoustic performance of a Helmholtz resonator may be modified considerably by the density and thickness of the fibrous material without changing the cavity dimensions.

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The acoustic performance of a dissipative expansion chamber lined with two concentric, annular layers of fibrous material with different resistances is investigated. A two-dimensional analytical approach is used to determine the transmission loss of this dissipative silencer. From the boundary conditions at the rigid wall, and the interfaces between the fibre layers and the central airway, the characteristic function and thus eigenvalues and eigenfunctions for sound propagation in the dissipative chamber are obtained, leading to transmission loss through application of pressure and velocity matching. The effects of geometry and fibre properties on the acoustic attenuation are also discussed.