Today, primarily porous absorbers such as fiber absorbers or pore elastic foams are applied for noise insulation, i. e. for decreasing the level of acoustic pressure. Their acoustic efficiency in components or assembly groups essentially depends on their material properties and their configuration. The determination of effective material properties on the basis of models of the microstructure of the porous absorbers, which is necessary for virtual material design, cannot yet be performed by any software tool; the effective material properties must therefore still be determined by complex measurements of work pieces or prototypes. For several years now, the Fraunhofer ITWM has worked on the development of methods for a drastic reduction of time and expenses with respect to the new development of absorber materials. Instead of measuring all the material parameters determining the acoustic properties of the material, these are entirely computed.

The method is based on a stochastic model representing the microstructure of the material very realistically. Already for some time now, it has been possible to determine the purely geometric material parameters for highly porous, inelastic absorbers, in order to simulate the propagation of airborne noise in the absorber by the models of Delany & Bazley or Allard & Johnson. Now, within the MEF project (individual research project focused on SMEs) "Characterization of acoustically effective pore elastic absorbers", a method has been developed and realized as the Acousto- Dict module within our software Geo- Dict which computes the effective (visco)elastic behavior of the porous absorber by additionally using the (visco) elastic properties of the material components, for example polyurethane. Thus, the computation of the coupled airborne and structure-borne noise can now be carried out easily by the model of Biot, for arbitrary absorber materials in the entire audible frequency domain from 100 Hz to 10,000 Hz.

In practical applications, for example concerning the interior lining of cars, several porous materials are usuallylaid one on top of another. The software AdOpt represents a tool for the designer which can help him/her to design and optimize the material layers; additionally, it provides a data base for the effective material parameters computed by AcoustoDict.

For reasons of validation, we have realized the interior roof lining of an Audi A6 by using the effective material parameters and the thickness of the individual layers in AdOpt; the acoustic behavior has been computed on the basis of the different acoustic models. A comparison with the measurement values shows that it is compulsory for low frequencies to account for the structureborne noise. The advantage of our method compared to all the other methods which have been available until now in the area of pore elastic absorbers is that the production of work pieces or prototypes becomes unnecessary.

The speed of sound c for a porous absorber is a frequency dependent
complex number. The most simple acoustic model of Delany and Bazley
(wich can only be applied to HIGHLY porous absorbers) states that

c = c_0 / (1+0.0978*C^{0.7000} - i*0.189*C^{0.595})

with C= sigma / (rho_0 * f) and

c_0    speed of sound of air
rho_0  density of air
sigma  flow resistance of the absorber in [kg/(m^3 s)] 
f      frequency of the acoustic wave

Note that we do not use the flow resistivity of the absorber sigma' but
that of the material, sigma = sigma' / (thickness of absorber).

For sigma->0 you get of course c->c_0. More details can be found here:

Acoustical properties of fibrous absorbent materials
Applied Acoustics, Volume 3, Issue 2, April 1970, Pages 105-116
M.E. Delany, E.N. Bazley