Civil Engineering Reference
In-Depth Information
11.2
Transfer matrix method
11.2.1 Principle of the method
Figure. 11.1 illustrates a plane acoustic wave impinging upon a material of thickness
h
,
at an incidence angle
θ
. The geometry of the problem is bidimensional, in the incident
(
x
1
,x
3
)
plane. Various types of wave can propagate in the material, according to their
nature. The
x
1
component of the wave number for each wave propagating in the finite
medium is equal to the
x
1
component
k
t
of the incident wave in the free air:
k
t
=
k
sin
θ
(11.1)
where
k
is the wave number in free air. Sound propagation in the layer is represented by
a transfer matrix [
T
] such that
V
(M)
=
[
T
]
V
(M
)
(11.2)
where
M
and
M
are set close to the forward and the backward face of the layer,
respectively, and where the components of the vector
V
(
M)
are the variables which
describe the acoustic field at a point
M
of the medium. The matrix [
T
] depends on the
thickness
h
and the physical properties of each medium.
11.3
Matrix representation of classical media
11.3.1 Fluid layer
The acoustic field in a fluid medium is completely defined in each point M by the vector:
=
[
p(M), v
3
(M)
]
T
V
f
(M)
(11.3)
x
3
h
x
1
θ
M
M´
finite medium
air
Figure 11.1
Plane wave impinging on a domain of thickness
h
.
