Civil Engineering Reference
In-Depth Information
2.5
semi-infinite layer
l = 5 cm
l = 3 cm
2
1.5
1
0.5
0
0
0.5
1
1.5
2
2.5
3
3.5
4
Frequency (kHz)
(p
t
−
Figure 7.18
|
in the pressure evalu-
ation with the modified formulation for different thicknesses. Material 2,
z
1
=
Modulus of the normalized error
|
p
t
)/p
t
z
2
=
−
2
.
5cm
,r
=
1m.
than for a thin layer. This can explain why the error decreases when the thickness
increases.
The normalized difference between the exact total pressure and the pressure predicted
with the modified formulation is shown in Figure 7.19 for a small angle of incidence. A
comparison is performed with the normalized difference between the exact total pressure
and the pressure
p
L
given by
exp
(
−
jk
0
R
2
)
R
2
exp
(
−
jk
0
R
1
)
R
1
p
L
=
+
V(
sin
θ
0
)
(7.69)
where the correction related to the sphericity of the source is omitted.
0.12
Modified formulation
Eq. (7.69)
0.1
0.08
0.06
0.04
0.02
0
0
1
2
3
4
Frequency (kHz)
Figure 7.19
Normalized error in the estimation of the total pressure with the modified
formulation and with Equation (7.69). Material 2,
l
=
2cm,
z
1
=
z
2
=−
0
.
5m
,r
=
1m.
