Low-frequency acoustic behavior of highly porous, layered, flexible, fine fiber materials

Abstract

This paper is concerned with predicting the acoustic behavior of highly porous, layered, flexible, fine fiber materials at low frequencies. A theoretical model of fiber behavior is developed that consists of two independent modes of vibration that exhibit resonance at zero frequency and a finite frequency. This model also incorporates a fiber parameter g that governs the fraction of fibers that can resonate which is now hypothesized to be frequency dependent and was found to range between a comparatively low value g0 near zero frequency and a high value g∞ at higher frequencies. These asymptotic values and the location of the transition region were found empirically. There is good agreement between this model and experiments designed to measure the effective resistivity φe and the effective density ρe of the fluid in the pores of the fibers over a wide range of frequencies.

The Acoustic Behaviors of Dual Layered Nonwoven Absorbers: From Model Building to Experiment Verification

“…5 Lambert proposed some linear systems to estimate the propagation characteristics of sound in fibrous porous both in fluid of the pores and in the elastic structural frame. [6][7][8][9] Ballagh deduced a function to explore the relationship between the flow resistivity, thickness and density of the fibrous material. 10 Voronina determined the sound absorption coefficient of a fibrous material layer by studying acoustic parameters such as the dimensionless characteristic impedance and propagation constants.…”

Fiber movements and sound attenuation in glass wool

“…The papers by Dahl et al 1 and Lambert 3,4 explain the measured acoustic properties by resonances in single fibers. However, it is difficult to see how single fiber could resonate, because all fibers are strongly coupled, and the wavelength of a sound wave are much longer than the distance between the fibers.…”

“…These resonances were caused by moving fibers. In a second paper 4 Lambert gave further data for resonances in the effective resistivity and the effective dynamic density.…”

Measurements of anisotropic sound propagation in glass wool

“…Tarnow 3 measured the propagation constants and characteristic impedance of glass wools for one direction of sound propagation. Lambert 4 presented dynamic resistivity data for Kevlar fiber material, where a resonance at 850 Hz was found. Voronina 5 gave data for glass, mineral, and basalt wool.…”