Civil Engineering Reference
In-Depth Information
8
Porous frame excitation by point
sources in air and by stress
circular and line sources - modes
of air saturated porous frames
8.1
Introduction
Some of the modes of air-saturated rigid framed porous layers have been described in
Chapter 7. These modes are related to poles of the plane wave reflection coefficient and
can be observed in the spherical reflected field at large angles of incidence. A real porous
structure is not motionless, but the results of Chapter 7 will not be noticeably modified,
for most of the porous media, if the Biot theory is used instead of a rigid-framed model.
In this chapter, the Biot theory is used to describe the frame displacement created by a
point source pressure field in air, or by a normal stress applied in a limited domain at the
surface of a layer. The porous media are supposed to be isotropic. Anisotropy effects are
considered in Chapter 10. A description of the displacement field created by a normal
stress field at the surface of the layers with a given wave number parallel to the surface is
discussed. The same description is performed when the stress field is replaced by a plane
pressure field in air. The Sommerfeld representation can be used to adapt the results to
the case of a point source in air. The Fourier transform or the Hankel transform can be
used for the case of a circular normal stress.
Another aim of this chapter is to present experiments which can be used to evaluate
the rigidity parameters of a porous frame in the audible frequency range. Many methods
of measuring the rigidity coefficients at very low frequencies have been carried out
