Civil Engineering Reference
In-Depth Information
6
Biot theory of sound propagation
in porous materials having an
elastic frame
6.1
Introduction
For many materials having an elastic frame and set on a rigid floor, as shown in
Figure 6.1(a), the frame can be almost motionless for large ranges of acoustical frequen-
cies, thus allowing the use of models worked out for rigid framed materials. Nevertheless,
this is not generally true for the entire range of acoustical frequencies. Moreover, for the
material set between two elastic plates represented in Figure 6.1(b), and for many other
similar situations, frame vibration is induced by the vibrations of the plates.
The transmission of sound through such a sandwich can be predicted only in the
context of a model where the air and the frame move simultaneously. Such a model is
provided by the Biot theory (Biot 1956) of sound propagation in elastic porous media.
Only the case of isotropic porous structures is considered in this chapter. In the context
of the Biot theory, the deformations of the structure related to wave propagation are
supposed to be similar to those in an elastic solid, i.e. in a representative elementary
volume there is no dispersion of the velocity in the solid part, in contrast to the velocity
in air. This leads to a description of the air - frame interaction very similar to that used
for rigid structures in Chapter 5.
6.2
Stress and strain in porous materials
6.2.1 Stress
In an elastic solid, or in a fluid, stresses are defined as being tangential and normal
forces per unit area of material. The same definition will be used for porous materials,
