The finite element (FE) and statistical energy analysis (SEA) methods have, respectively, high and low frequency limitations and there is therefore a broad class of “mid-frequency” vibro-acoustic problems that are not suited to either FE or SEA. A hybrid method combining FE and SEA was recently presented for predicting the steady-state response of vibro-acoustic systems with uncertain properties. The subsystems with long wavelength behavior are modeled deterministically with FE, while the subsystems with short wavelength behavior are modeled statistically with SEA. The method yields the ensemble average response of the system where the uncertainty is confined in the SEA subsystems. This paper briefly summarizes the theory behind the method and presents a number of detailed numerical and experimental validation examples for structure-borne noise transmission.

1.
M. S.
Kompella
and
B. J.
Bernhard
, “
Measurement of the statistical variation of structural-acoustic characteristics of automotive vehicle
,” in
Proceedings of the SAE Noise and Vibration Conference
, Warrendale PA (
1993
).
2.
R.
Cornish
, “
A novel approach to optimizing and stabilizing interior noise quality in vehicles
,”
Proceedings of the Institute of Mechanical Engineers, Part D –
J. Automobile Eng.
214
(
D7
),
685
692
(
2000
).
3.
R. H.
Lyon
and
R. G.
DeJong
,
Theory and Application of Statistical Energy Analysis
(
Butterworth-Heinemann
, Boston
1995
).
4.
R. S.
Langley
and
V.
Cotoni
, “
Response variance prediction in the statistical energy analysis of built-up systems
,”
J. Acoust. Soc. Am.
115
(
2
),
706
718
(
2004
).
5.
A. K.
Belyaev
and
V. A.
Palmov
, “
Integral theories of random vibration of complex structures
,” in
Random Vibrations – Status and Recent Developments
, edited by
I.
Elishakoff
and
R. H.
Lyon
(
Elsevier
, Amsterdam,
1986
).
6.
C.
Soize
, “
A model and numerical method in the medium frequency range for vibroacoustic predictions using the theory of structural fuzzy
,”
J. Acoust. Soc. Am.
94
(
2
),
849
865
(
1993
).
7.
R. S.
Langley
and
P.
Bremner
, “
A hybrid method for the vibration analysis of complex structural-acoustic systems
,”
J. Acoust. Soc. Am.
105
(
3
),
1657
1671
(
1999
).
8.
V.
Jayachandran
and
M. W.
Bonilha
A hybrid SEA/modal technique for modeling structural-acoustic interior noise in rotorcraft
,”
J. Acoust. Soc. Am.
113
(
3
),
1448
1454
(
2003
).
9.
R. M.
Grice
and
R. J.
Pinnington
, “
Analysis of the flexural vibration of a thin-plate box using a combination of finite element analysis and analytical impedances
,”
J. Sound Vib.
249
(
3
),
499
527
(
2002
).
10.
L.
Ji
,
B. R.
Mace
, and
R. J.
Pinnington
, “
A mode-based approach for the mid-frequency vibration analysis of coupled long- and short-wavelength structures
,”
J. Sound Vib.
289
(
1-2
),
148
170
(
2006
).
11.
S. B.
Hong
,
A.
Wang
, and
N.
Vlahopoulos
, “
A hybrid finite element formulation for a beam-plate system
,”
J. Sound Vib.
298
(
1-2
),
233
256
(
2006
).
12.
P. J.
Shorter
and
R. S.
Langley
, “
Vibro-acoustic analysis of complex systems
,”
J. Sound Vib.
288
(
3
),
669
699
(
2005
).
13.
P. J.
Shorter
and
R. S.
Langley
, “
On the reciprocity relationship between direct field radiation and diffuse reverberant loading
,”
J. Acoust. Soc. Am.
117
(
1
),
85
95
(
2005
).
14.
R. S.
Langley
, “
On the diffuse field reciprocity relationship and vibrational energy variance in a random subsystem at high frequencies
,”
J. Acoust. Soc. Am.
121
(
2
),
913
921
(
2007
).
15.
R. S.
Langley
and
V.
Cotoni
, “
Prediction of the ensemble mean and variance of the response of uncertain structures using the Hybrid FE-SEA method
,” in
Proceedings of ISMA2006 Conference
, Leuven, Belgium, September 18–20 (
2006
).
16.
R. S.
Langley
and
P. J.
Shorter
, “
The wave transmission coefficients and coupling loss factors of point connected structures
,”
J. Acoust. Soc. Am.
113
(
4
),
1947
1964
(
2003
).
17.
R. S.
Langley
,
P. J.
Shorter
,
R. H.
Lande
, and
V.
Cotoni
, “
Hybrid deterministic-statistical modeling of built-up structures
,” in
Proceedings of ICSV12 Conference
, Lisbon, Portugal, July 11–14 (
2005
).
18.
R. S.
Langley
, “
Natural frequency statistics and universality
,” in
Proceedings of ICSV12 Conference
, Lisbon, Portugal, July 11–14 (
2005
).
19.
VA ONE 2006 User’s Guide, The ESI Group Oct.
2006
.
20.
B. R.
Mace
and
P. J.
Shorter
, “
Energy flow models from finite element analysis
,”
J. Sound Vib.
233
(
3
),
369
389
(
2000
).
21.
R. S.
Langley
and
K. H.
Heron
, “
Elastic wave transmission through plate/beam junctions
,”
J. Sound Vib.
143
(
2
),
241
253
(
1990
)
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