A Model for Calculating the Noise Absorption Capacity of Nonwoven Fiber Webs

Abstract

Nonwovens can be used as noise control elements for a wide range of applications. This paper suggests a numerical method for calculating their acoustic performance using the theory of Zwikker and Kosten on sound propagation through porous media. The results for nonwovens made from acrylic fibers, cotton, and polyester are in fair agreement with experimental findings. The model yields the noise absorption coefficients of fiber webs as a function of their thickness and porosity. This relationship might serve as a guideline for the optimal design of passive control components made of nonwovens.Nonwoven fiber webs can be considered as noise control elements for a wide range of applications, such as acoustic ceilings and barriers, carpets, and wall claddings [5,6,9,10]. Experimental studies indicate that the noise absorption and insulation'capacities of such elements are competitive with known sound-proofing materials [7]. However, the optimal design of acoustic assemblies made of textiles calls for a theoretical model with the power of predicting the noise absorption coefficients of the nonwoven medium as a function of its thickness, porosity, fiber content, and other intrinsic characteristics.Since the advent of the monumental work of Zwikker and Kosten [ I 1 ] on sound transfer through porous media, several models assuming some symmetry in fibrous material have been suggested. Dahl et al. t I ] examined materials made of cylindrically shaped fibers arranged in a batting, with the fibers primarily aligned parallel to the face of the batting. Lambert [3,4] developed a model for high porosity Kevlar consisting of long flexible fibers that are usually layered and display a pronounced resonant effect.Such approximations are inadequate for the random mixture of fibers and air pores in a nonwoven fiberweb. A more appropriate model was suggested by Dent [2], who elaborated on the theory of Zwikker and Kosten. According to his model, a nonwoven is composed of air and fiber phases that react differently with the sound wave. The mathematical solution of the basic equations indicates that there are two forward and two backward waves traveling through both phases of the fiber web. The objective of our paper is to use Dent's work to calculate the noise absorption coefficients of some nonwovens. Although our approach for solving the boundary value problem associated with this model is different than Dent's, it yields the same analytical results. Basic Equations and Boundary ConditionsIn.tis section, we review briefly the essentials of the Zwikk~.r and Kosten theory [ I I ] relevant to our discussion. We use Dent's notations here [2].Let ?~ and p~ be the densities of air and fiber per unit volume of the fiberweb, po and pp the densities of free air and polymeric material, and v~ and vf = 1 -vQ the volume fraction of air and fiber, respectively. Then p, v,,po and p~ = Vfpp.The two equations of motion for infinitesimal elements of fiber and air are, respectively (ignoring viscous forces), and where the subscripts a and f refer to th...

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

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