Civil Engineering Reference
In-Depth Information
usually been neglected. The classical approximation for modelling free field radiation
of porous materials assumes the total stress tensor and the interstitial pressure at the
radiation surface to be zero (Debergue
et al
. 1999). In this case, it is assumed that the
surface impedance of the solid phase is much higher than the impedance of the surround-
ing acoustic medium, and in consequence the porous system is assumed to be vibrating
in vacuum. Other methods use a plane wave approximation in the same manner as is
classically done in the transfer matrix method (Chapter 11). This is mainly acceptable
at high frequencies, but is clearly erroneous at low frequencies. These approximations
can be alleviated for specific problems. In the case of radiation of a porous medium
in a waveguide, the radiation impedance can be calculated accurately by expressing the
radiated pressure in terms of the modal behaviour of the waveguide (Section 13.4.7).
In the case of a thin porous plate under flexural vibration, Horoshenkov and Sakagami
(2000) considered the absorption and transmission problems and presented a parametric
study on the influence of the porous plate parameters on its absorption. Takahashi and
Tanaka (2002) considered the same problem and presented an analytical model to calcu-
late the radiation impedance of a thin porous plate in flexure; in particular, they discussed
the effects of plate permeability on its radiation damping based on numerical examples.
Atalla
et al
. (2006) presented a formulation, based on the mixed displacement - pressure
formulation, for evaluating the sound radiation of baffled poroelastic media in the special
case where the material surface is baffled. It expresses the free field condition using
Rayleigh's integral, in terms of an added admittance matrix and a solid phase - interstitial
pressure coupling term. The approach is general and easy to implement. It can handle
situations such as planar multilayer systems with various excitations. Numerical results
were presented to illustrate the accuracy of the method. A recall of this formulation is
presented here.
Consider the coupling of a planar baffled porous domain with a semi-infinite fluid
(Figure 13.4). In the
(
u
s
,p)
formulation, the porous medium couples to the semi-infinite
fluid medium through the boundary term given by Equation (13.8). Since at the free
surface:
σ
ij
n
j
=−
pn
i
, Equation (13.8) becomes:
δ
pu
s
n
d
S
φ
u
n
−
u
s
n
+
u
s
n
δp
d
S
I
p
=
−
(13.59)
Figure 13.4
Radiation from a flat baffled poroelastic material.
