Civil Engineering Reference
In-Depth Information
Next the various vibroacoustic indicators are calculated using the methodology
described for the point load. For example, consider an isotropic panel with attached
isotropic layered material. Let
V(ξ
1
,ξ
2
)
and
Z(ξ
1
,ξ
2
)
be the plane wave reflection
coefficient and normal impedance at the free face of the excited panel (
z
2
=
0inFigure
7.1). Using symmetry, both these quantities only depend on
ξ
(ξ
1
+
ξ
2
)
1
/
2
,andthe
=
normal velocity
v
reads (see Section 7.1)
j
∞
0
1
+
V(ξ/k
0
)
Z(ξ/k
0
)µ
J
0
(rξ)
exp[
jµz
1
]
ξ
d
ξ
υ(r)
=−
(12.61)
The pressure at the observer location (see Figure 7.1) is given by
j
∞
0
1
+
V(ξ/k
0
)
µ
p(r)
=−
J
0
(rξ)
exp[
jµ(z
1
+
z
2
)
]
ξ
d
ξ
(12.62)
Methods to evaluate Equations (12.61) and (12.62) are discussed in Chapter 7 in the
context of a porous layer excited by a point source.
12.6
Other applications
As demonstrated in the previous sections, the transfer matrix method can be used to
compute vibroacoustic indicators of practical interest, such as air-borne insertion loss,
structure-borne insertion loss and damping added by a sound package. In turn these
indicators, with the diffuse field absorption and the transmission loss, can be used within
SEA framework to account for the effect of sound package in full system configurations,
such as cars or aircraft (Pope
et al
. 1983, Atalla
et al
. 2004). Assuming that the trim
(sound package) covers the area
A
t
of the panel and the remaining area
A
b
=
A
−
A
t
is
bare, the noise reduction of the panel is given by:
τ
f
+
η
rad
A
b
η
αA
t
+
τ
r
NR
=
10 log 10
(12.63)
τ
t
τ
b
A
t
+
τ
b
A
b
where
η
is the sum of the space and band averaged radiation loss factor,
η
rad
,ofthe
panel and its averaged structural loss factor,
η
s
;
τ
f
is the field incidence non-resonant
transmission coefficient (mass controlled),
τ
r
is the diffuse field resonant transmission
coefficient,
τ
b
τ
r
,τ
t
is the transmission coefficient of the trim, and finally
α
is
the random incidence trim absorption coefficient. Both
α,τ
t
and the trim's contribution
to
η
2
are estimated numerically using the TMM. For curved panels, the sound package
is simply 'unwrapped' and the TMM is used to calculate the sound package absorption,
transmission loss, insertion loss, absorption and added damping. This is a current limi-
tation of the method. Its generalization to curved sound packages is still an open issue.
Recent finite element and experimental studies show that curvature should be accounted
for in the calculation of the insertion loss of a sound package (Duval
et al
. 2008). One can
argue, however, that curvature effect will be mainly important before the ring frequency
of the panel. This explains why the use of the flat panel assumption is sufficient for
aircraft applications. For highly curved panels, such as wheel houses in an automotive,
an accurate approach should be used. Similarly to the TMM-modal discussion of the
=
τ
f
+
