On the modeling of sound radiation from poroelastic materials

Abstract

Numerical approaches based on finite element discretizations of Biot's poroelasticity equations provide efficient tools to solve problems where the porous material is coupled to elastic structures and finite extent acoustic cavities. Sometimes, it may be relevant to evaluate the radiation of a poroelastic material into an infinite fluid medium. Examples include ͑i͒ the evaluation of the diffuse field sound absorption coefficient of a porous material and/or the sound transmission loss of an elastic plate coupled to a porous sheet, ͑ii͒ the assessment of the acoustic radiation damping of a porous material coupled to a vibrating structure. The latter is particularly important for the correct experimental characterization of the intrinsic damping of the material's frame. Up to now, the acoustic radiation of a porous medium into an unbounded fluid medium has usually been neglected. The classical approaches for modeling free field radiation of porous materials ͑i͒ assumes the interstitial pressure at the radiation surface to be zero or ͑ii͒ fixes the radiation impedance to an approximate value. This paper discusses the limitations of these assumptions and presents a numerical formulation for evaluating the sound radiation of baffled poroelastic media including fluid loading effects. The problem is solved using a mixed FEM-BEM approach where the fluid loading is accounted for using an admittance matrix. Both numerical examples and a transmission loss test are presented to illustrate the performance of the technique and its applications.

A simple method to account for size effects in the transfer matrix method

“…(29), it is important to note that the infinite limit of integration for the wavenumber is important to correctly capture the behavior below the critical frequency of (17) is important compared to a direct evaluation of Eq. (15) as done previously (Atalla et al, 2006). Figure 2 shows a comparison between the radiated power calculated using Eq.…”

“…It consists of a flat 1.64 m ϫ 1.19 m ϫ 1.016 mm aluminum panel with 7.62 cm thick attached foam. The description of the test and the finite element calculation are given in Atalla et al (2006). The measured transmission loss and predictions with the FTMM are given in Fig.…”

“…To account for size effects, the FTMM proposes to replace the infinite size transmission coefficient by a finite size coefficient given by f = ϱ ͑ R cos ͒, where R is homogeneous to radiation efficiency and is given by (Atalla et al, 2006) a͒ Author to whom correspondence should be addressed.…”

“…The rationale behind both approaches is to replace the "infinite size" radiation efficiency in the receiving medium, by the radiation efficiency of an equivalent baffled window. The Rayleigh-integral based method, referred to by the finite transfer matrix method (FTMM), has been used by Atalla et al (2006) to solve both the diffuse field transmission loss and absorption of flat multilayer structures. Various experimental examples were presented by the previous authors to corroborate the validity of the proposed methods.…”

Fuzzy structure theory modeling of sound-insulation layers in complex vibroacoustic uncertain systems: Theory and experimental validation

“…In this case, both vibroacoustic system and sound-insulation layers are modeled by the finite element method (see for instance Refs. [1][2][3][4][5][6][7]). When the first thickness eigenfrequencies belong to the frequency band of analysis, as assumed here, such a finite element model of sound-insulation layer introduces a large number of physical degrees of freedom (DOF) in the computational model as well as numerous elastic modes in the band.…”