Civil Engineering Reference
In-Depth Information
Fluid 1
(1)
(2)
(n)
Fluid 2
M
2n-1
A
M
1
M
2
M
3
M
4
M
2n
B
Figure 11.5
A multilayer domain backed by a semi-infinite fluid.
=
[
p(B)v
3
(B)
]
T
and [
I
(n)f
]and[
J
(n)f
] are interface matrices which
depend on the nature of the last layer (
n)
.Furthermore,if
Z
B
is the characteristic
impedance of the semi-infinite fluid, the impedance at point
B
is given by
Z
B
/
cos
θ
where
V
f
(B)
=
p(B)/v
3
(B)
,or
1
Z
B
/
cos
θ
]
V
f
(B)
[
−
=
0
(11.84)
Equations (11.83) and (11.84) lead to a new matrix system
[0]
.
.
.
[0]
[
D
0
]
[
D
]
V
=
0:[
D
]
=
,
[0]
···
[0]
[
I
(n)f
]
[
J
(n)f
]
0
···
0
−
1
Z
B
/
cos
θ
V
f
(A)
V
(
1
)
(M
2
)
V
(
2
)
(M
4
)
.
.
.
V
(n
−
1
)
(M
2
n
−
2
)
V
(n)
(M
2
n
)
V
f
(B)
V
0
V
f
(B)
V
=
=
(11.85)
Counting the added equations and variables, matrix [
D
] has now (
N
+
1) rows and
(
N
2) columns. In summary, for both termination conditions, one equation is still
needed. This equation is given by the impedance condition of the fluid at the excita-
tion side. Adding this equation to matrix [
D
] allows for the calculation of the acoustic
indicators of the problem.
+
