Design optimization of porous fibrous material for maximizing absorption of sounds under set frequency bands

In this paper, a methodology is proposed for designing porous fibrous material with optimal sound absorption under set frequency bands. The material is assumed to have a rigid frame and a hexagonal arrangement of fibers, and the analytical model derived by Johnson, Champoux and Allard (“JCA model”) is used to investigate the influences of the micro-structural parameters (fiber radius r and gap w) on sound absorption performance, and the macro-acoustic parameters used in JCA model is determined via finite element analysis for the hexagonal micro-structure. Moreover, a mathematical model is constructed to obtain the optimized micro-structure design, with fiber radius and gap as design parameters and average absorption performance of the porous fibrous material under set frequency band as target. Utilizing the constructed optimization model, the microstructure parameters are derived with optimal sound absorption under low frequency (20 ⩽ f < 500 Hz), medium frequency (500 ⩽ f < 2000 Hz) and high frequency (2000 ⩽ f < 15,000 Hz), respectively. On top of that, for a given thickness of porous fibrous material layer, the analytical relationship between fiber radius and optimal porosity under set frequency bands is constructed.