On the acoustic analysis and design of porous materials for low-frequency noise control

Abstract

Porous materials are common sound absorption materials, which are widely used in passive noise control. This thesis focuses on the acoustic analysis of porous materials, based on which, the structural design and parameter optimization are conducted for different application situations. Firstly, a periodic corrugated waveguide (PCWG) structure is proposed and analyzed with the wave finite element (WFE) method through a homogenization process. The PCWG structure is shown to add tortuosity to the waveguide, hence higher equivalent fluid density is achieved, while the system elastic modulus remains unchanged. The added tortuosity enhances the broadband, low-frequency sound absorption by increasing the equivalent mass without the corresponding increase of excess damping, the latter being partly responsible for the poor performance for usual absorber in the low-frequency region. The proposed PCWG structure provides another dimension in design and optimization of porous materials besides the flow resistivity. An optimization example shows that for the given length of 0.1m, and given frequency range of [125Hz, 500Hz], the sound absorption coefficient of porous materials is improved with PCWG over the entire frequency range of interest. Then a gradient design of porous materials is proposed, which can achieve better sound absorption property than the uniform material through better impedance match. As an application example of the gradient porous materials, a uniform-then-gradient, flat-wall (UGFW) structure is designed for the decoration of the anechoic chamber, and compared with the classical wedge design. With the modified anechoic chamber simulation model, it is found that the UGFW structure can achieve better performance than the traditional wedge structure in an anechoic chamber with smaller decoration depth. A macro-void design is hence proposed, as a method to realize such gradient porous material. For the macro-void design, the macro porosity distribution is optimized through the direct simulation of the anechoic chamber with the help of equivalent fluid parameters. It is found that, compared with the wedge structure, the gradient void design can save the decoration depth by 15%, while achieving better performance, for a fixed chamber dimension of 9m*8m*7m (from tip to tip) and designed cut-off frequency of 100Hz. Finally, a poroelastic lined duct is analyzed with the eigenmodes of the cross-section, obtained through the WFE approach. The acoustic characteristics of poroelastic lined duct is analyzed with emphasis on the effect of skeleton elasticity. For the structure-borne modes, a strong coupling between the fluid phase and solid phase is observed; while for the fluid-borne modes, such coupling is found to be negligible. For a poroelastic lined duct silencer, it is found that the structure-borne mode accounts for the low-frequency spectral peaks in transmission loss spectrum through enhanced absorption and reflection effect. Meanwhile, the change of boundary condition of the poroelastic material has significant effect on the structure-borne mode. In the simulated case, the change of boundary condition from fixed to rolling causes the first structure-borne mode to change from a non-propagating high-order-like mode to a propagating plane-wave-like mode in low-frequency range, which affects the acoustic characteristics of the poroelastic lined silencers noticeably.