Civil Engineering Reference
In-Depth Information
10
Transversally isotropic poroelastic
media
10.1
Introduction
Fibrous media, glass wools and rockwools, are strongly anisotropic. Currently, due to the
manufacturing process, they can be considered as transversally isotropic media (Tarnow
2005), with an axis of symmetry perpendicular to the faces of the layers. It has been shown
by Melon
et al
. (1998) that porous foams can also present a noticeable anisotropy which
is more complex, but in a first approach, the frame in vacuum can be considered as a
transversally isotropic elastic medium. A more precise description is given by Liu and Liu
(2004) with orthotropy, but it will not be easy to measure the numerous parameters used in
the description. In an anisotropic medium the wave numbers of the different waves depend
on the direction of propagation, or for instance on the wave number vector components
at the surface of the medium. The source can often be defined by a spectrum of wave
number components at the surface of the medium, and this last characterization of the
wave number components or of the slowness components simplifies the prediction of the
induced displacement field. In Sections (10.2) - (10.5) wave propagation in transversally
isotropic media is described in a similar way as in the works by Sharma and Gogna (1991),
and Vashishth and Khurana (2004), where the different waves are defined for given wave
number components at the surface and where the symmetry axis is perpendicular to the
surface. Sections (10.5) - (10.6) are concerned with the field created by a sound source
in air and by a mechanical excitation, and with rigid-framed media. In Section (10.7),
the case of a transversally isotropic porous medium with the axis of symmetry in an
orientation different from the normal to the faces is considered. The Rayleigh surface
waves in directions parallel and perpendicular to the axis of symmetry are described in
Section (10.8). In Section (10.9) a matrix representation of transversally isotropic porous
layers is given.
