Civil Engineering Reference
In-Depth Information
5
0
−
5
−
10
−
15
−
20
FTMM (Eq. 12.10)
Leppington (asymptotic)
−
25
10
2
10
3
10
4
Frequency(HZ)
Figure 12.2
Radiation efficiency of a plate in bending. Comparison between Leppington
asymptotic formulas and Equation (12.10) with
k
t
in Equation (12.11) replaced by the
plate bending wave number.
12.2.2 Transmission coefficient
By analogy with the infinite case, the transmitted power, Equation (12.12), is written
1
2
S
cos
θ
ρ
0
c
τ
f
t
=
2
the energy transmission coefficient accounting for the finite size effect.
It is related to the classical coefficient
τ
∞
with
τ
f
=|
T
f
|
by
τ
f
=
τ
∞
(σ
R
cos
θ)
(12.17)
The associated diffuse field transmission coefficient is given by
π/
2
2
π
τ
f
(θ,φ)
sin
θ
cos
θ
d
φ
d
θ
0
0
τ
f_diff
=
(12.18)
π/
2
2
π
sin
θ
cos
θ
d
φ
d
θ
0
0
Villot
et al
. (2001) suggest the use of the same size correction for the incident power,
leading to
τ
∞
(σ
R
cos
θ)
2
τ
f
=
(12.19)
