Civil Engineering Reference
In-Depth Information
If
K
and
F
n
are rewritten in terms of
u
and
u
exp
j
k
0
L
x
2
r
2
1
/
2
u
2
u
2
=
exp
u
cos
ϕ
r
sin
ϕ
+
u
j
k
t
L
x
2
K
(u,u
)
F
n
(u,u
)
=
;
−
+
u
2
r
2
1
/
2
u
2
+
(12.A.8)
Equation (12.A.6) leads to
d
v
K
(u,u
)
d
u
d
v
K
(u,u
)
d
u
=
2
2
2
−
u
0
2
2
u)
K
(u,u
)
d
u
+
(
2
−
0
0
−
2
−
u
0
(12.A.9)
Using these transformations the radiation impedance becomes:
2
2
jρ
0
ω
L
y
4
π
u
)
K
(u,u
)F
n
(u,u
)
d
u
d
u
Z
=
(
2
−
u)(
2
−
(12.A.10)
0
0
1and
u
→
u
+
Finally, the change of variables
u
→
u
+
1isusedtotransformthe
integration domain into [ - 1,1] :
1
1
jρ
0
ω
L
y
4
π
u
)
K
(u
+
1
,u
+
1
,u
+
1
)
d
u
d
u
Z
=
(
1
−
u)(
1
−
+
1
)F
n
(u
−
1
−
1
(12.A.11)
This last integral can be evaluated numerically.
References
Atalla, N., Ghinet, S. and Haisam, O. (2004) Transmission loss of curved sandwich composite
panels.
18th ICA
, Kyoto.
Duval, A., Dejaeger, L., Baratier, J. and Rondeau, J-F (2008) Structureborne and airborne Insertion
Loss simulation of trimmed curved and flat panels using Rayon-VTM-TL: implications for
the 3D design of insulators.
Automobile and Railroad Comfort
- November 19 - 20, Le Mans,
France.
Ghinet, S. and Atalla, N. (2002) Vibro-acoustic behaviour of multi-layer orthotropic panels.
Cana-
dian Acoustics
30
(3) 72 - 73.
Ghinet, S. and Atalla, N. (2006) Vibro-acoustic behaviours of flat sandwich composite panels.
Transactions of Canadian Soc. Mech. Eng J
.
30
(4).
Leppington, F.G., Broadbent, E.G., & Heron, K.H. (1982) The acoustic radiation efficiency from
rectangular panels. Proc. R. Soc. London.
382
, 245.
Leppington, F. G, Heron, K. H. & Broadbent, E. G. (2002) Resonant and non-resonant noise
through complex plates.
Proc. R. Soc. Lond
.
458
, 683 - 704.
Nelisse, H., Onsay, T. and Atalla, N. (2003) Structure borne insertion loss of sound package com-
ponents.
Society of Automotive Engineers
, SAE paper 03NVC-185, Traverse City, Michigan.
