Civil Engineering Reference
In-Depth Information
10
abs(1/cos(
θ
))
8
100 Hz
500 Hz
1000 Hz
2000 Hz
5000 Hz
6
4
2
0
−
2
−
4
−
6
−
8
−
10
0
0.5
1
1.5
2
2.5
3
radiation angle (
θ
)
Figure 12.1
Variation of the heading averaged geometrical radiation efficiency with
incidence angle at selected frequencies for a 1
×
0
.
8 m rectangular window.
An alternative finite size correction is given by Villot
et al
. (2001). It is based on the
same assumptions and is derived in wave number domain. It is referred to in the literature
as a 'windowing' correction. It leads to the following expression for the correction factor:
k
0
2
π
1
−
cos
((
k
r
cos
ψ −
k
t
cos
ϕ
)
L
x
)
[
(
k
r
cos
ψ −
k
t
cos
ϕ
)
L
x
]
2
S
π
σ
R
(
k
t
,
ϕ
)
=
2
0
0
(12.16)
−
)
L
y
)
[
(
k
r
sin
ψ −
k
t
sin
ϕ
)
L
y
]
2
cos
((
k
r
sin
ψ −
ϕ
1
k
t
sin
k
0
k
r
k
0
−
×
×
d
ψ
dk
r
k
r
Comparison of the numerical evaluation of Equation (12.15) using the two approaches
leads to similar results. However, the approach presented here is preferred due to its
computational efficiency.
In the special case where the trace wave number
k
t
k
0
sin
θ
is replaced by the
bending wave number of a given structure, Equations (12.10) and (12.11) lead to the
radiation efficiency of the structure for this particular wave. For instance, Figure 12.2
gives an example of a 5-mm-thick, simply supported rectangular aluminum plate measur-
ing 1
.
=
(
√
ω
4
√
m/D)
with
D
the bending stiffness and
m
the surface mass density. The radiation efficiency
obtained is compared with estimation using Leppington's asymptotic formulas (Lepping-
ton
et al
. 1982). Good correlation is observed between the two methods.
×
0
.
8 m and having a critical frequency of 2350 Hz. In this case,
k
t
=
