Civil Engineering Reference
In-Depth Information
The pressure
p
in the fibrous material has the form
p(x
1
,x
2
,x
3
,t)
=
A
exp[
j(
−
k
1
x
1
−
k
3
x
3
+
ωt)
]
A
exp[
j
+
−
(k
1
x
1
+
k
3
x
3
+
ωt)
]
(3.58)
The component of velocity in the
x
3
direction obtained from Eq. (3.55) is
1
(ρ
N
K)
1
/
2
k
3
k
N
[
A
exp[
j(
υ
3
(x
1
,x
2
,x
3
,t)
=
−
k
1
x
1
−
k
3
x
3
+
ωt)
]
A
exp[
j(
−
−
k
1
x
1
+
k
3
x
3
+
ωt)
]]
(3.59)
A
.At
x
3
At
x
3
=
0,
v
3
=
0, and
A
=
=−
d
, the impedance
Z
is equal to
Z
=
(ρ
N
K)
1
/
2
k
N
k
3
(
−
j
cotg
k
3
d)
(3.60)
The laws of Delany and Bazley, Equations (2.28) and (2.29), can be used to evaluate
the characteristic impedance
(ρ
N
K)
1
/
2
and
k
N
from the normal flow resistivity, as well
as
k
P
, that is used in Equation (3.57), from the planar flow resistivity. The evaluation of
the reflection coefficient and the absorption coefficient is the same as in Section 3.5.
1000
500
0
Re Z: s = 1
Re Z: s = 0.6
Re Z: s = 0.3
Im Z: s = 1
Im Z: s = 0.6
Im Z: s = 0.3
−
500
−
1000
−
1500
0
10
20
30
40
50
60
70
80
90
q
(deg)
Figure 3.12
Predicted impedance
Z
in Pa m
−
1
s versus the angle of incidence
θ
in
degrees for three values of the anisotropy factor
s
=
σ
P
/σ
N
.
