This paper presents a modal approach to calculate the acoustic normal modes in complex ducts. In this study, the component modal synthesis (CMS) method in two dimensions for application in large duct with acoustic propagation in order to obtain a reduced acoustic model will be developed. The proposed technique is based on division of the acoustic system in well-known modal model subdomains and uses a CMS procedure to obtain a reduced acoustic modal model of the large system. In this paper, the applicability of the CMS Craig-Chang's method was adapted for acoustics CMS, considering only acoustic fluid interaction. In the modal synthesis technique developed originally for structural purpose, displacements and forces were coupled at the boundary of the substructures by dynamic constraint equations. The methodology developed here is based on residual flexibility, using residual inertia relief attachment modes in place of simply residual attachment modes to couple sound pressure and flow rates at the substructures interfaces. The approach leads to a versatile method with a low computational cost. To validate the proposed CMS approach, comparison with acoustic ducts models using finite element methodology (FEM) and analytical solutions were made. The differences between the analytical and numerical results as well as the limitations and advantages of each method were discussed.

References

References
1.
Blazier
, Jr.,
W. E.
,
1997
, “
A Refined Procedure for Rating the Noise of Heating, Ventilating and Air-Conditioning (HVAC) Systems in Buildings
,”
Noise Control Eng. J.
,
45
(
6
), pp.
243
150
.10.3397/1.2828446
2.
Barron
,
R. F.
,
2003
,
Industrial Noise Control and Acoustic
,
Marcel Dekker
,
New York
, pp.
192
195
.
3.
Magalhães
,
M. D. C.
, and
Ferguson
,
N. S.
,
2003
, “
Acoustic–Structural Interaction Analysis Using the Component Mode Synthesis Method
,”
Appl. Acoust.
,
64
, pp.
1049
1067
.10.1016/S0003-682X(03)00068-9
4.
Masson
,
G.
,
Ait Brik
,
B.
,
Cogan
,
S.
, and
Bouhaddi
,
N.
,
2006
, “
Component Mode Synthesis (CMS) Based on an Enriched Ritz Approach for Efficient Structural Optimization
,”
J. Sound Vib.
,
296
, pp.
845
860
.10.1016/j.jsv.2006.03.024
5.
Smirnova
,
T.
,
Larsson
,
M.
,
Gertsovich
,
I.
,
Johansson
,
S.
,
Claesson
,
I.
, and
Håkansson
,
L.
,
2010
, “
Initial Investigations Concerning Modeling of Sound Propagation in Ducts With ANC by Means of Two-Port Theory and FEM
,”
Proceedings of the 17th International Congress on Sound and Vibration (ICSV17)
,
Cairo, Egypt
, pp.
1
8
.
6.
Kühnelt
,
H.
,
Bäuml
,
T.
, and
Haumer
,
A.
,
2009
, “
Soundductflow: A Modelica Library for Modeling Acoustics and Flow in Duct Networks
,”
Proceedings 7th Modelica Conference
,
Como, Italy
, pp.
519
525
.
7.
Craig
, Jr.,
R. R.
, and
Chang
,
C. J.
,
1976
, “
Free-Interface Methods of Substructure Coupling for Dynamic Analysis
,”
AIAA J.
,
14
(
11
), pp.
1633
1635
.10.2514/3.7264
8.
Craig
, Jr.,
R. R.
,
2000
, “
A Brief Tutorial on Substructure Analysis and Testing, Proceedings of the 18th International Modal Analysis
,”
Conference on Computational Challenges in Structural Dynamics
,
San Antonio, TX
, pp.
899
908
.
9.
Craig
, Jr.,
R. R.
, and
Chang
,
C. J.
,
1977
, “
On the Use of Attachment Modes in Substructure Coupling for Dynamic Analysis
,”
Proceedings of the 18th Structures, Structural Dynamics and Materials Conference
,
San Diego, CA
, pp.
89
99
.
10.
Magalhães
,
M. D. C.
, and
Ferguson
,
N. S.
,
2005
, “
The Development of a Component Mode Synthesis (CMS) Model for Three-Dimensional Fluid–Structure Interaction
,”
J. Acoust. Soc. Am.
,
118
(
6
), pp.
3679
3690
.10.1121/1.2114567
11.
MacNeal
,
R. H.
,
1971
, “
A Hybrid Method of Component Mode Synthesis
,”
Comput. Struct.
,
1
(
4
), pp.
581
601
.10.1016/0045-7949(71)90031-9
12.
Rubin
,
S.
,
1975
, “
Improved Component-Mode Representation for Structural Dynamic Analysis
,”
AIAA J.
,
13
(
8
), pp.
995
1006
.10.2514/3.60497
13.
Blevins
,
R. D.
,
1979
,
Formulas for Natural Frequency and Mode Shape
,
Krieger
,
Malabar, FL
, pp.
337
350
.
14.
Craig
, Jr.,
R. R.
, and
Chung
,
Y. T.
,
1981
, “
Generalized Substructure Coupling Procedure for Damped Systems
,”
AIAA J.
,
20
(
3
), pp.
442
444
.10.2514/3.51089
15.
Duarte
,
M. A. V.
,
1994
, “
Ajuste de Modelos Dinâmicos de Estruturas com não Linearidades Concentradas (Dynamic Models Adjustment of Structures With Nonlinearities Concentrated)
,” Ph.D. thesis, Universidade de Campinas-UNICAMP, Campinas-SP, Brazil.
16.
Hansen
,
C. H.
, and
Snyder
,
S. D.
,
1997
,
Active Control of Noise and Vibration
,
Taylor and Francis
,
London
, pp.
597
599
, Chap. 7.
17.
Morse
,
P. M.
, and
Ingard
,
K. U.
,
1968
,
Theoretical Acoustic
,
McGraw-Hill
,
New York
, pp.
467
576
.
18.
Zander
,
A. C.
, and
Hansen
,
C. H.
,
1993
, “
A Comparison of Error Sensor Strategies for the Active Control of Duct Noise
,”
J. Acoust. Soc. Am.
,
94
, pp.
841
848
.10.1121/1.408185
19.
Beranek
,
L. L.
, and
Vér
,
I. L.
,
1992
,
Noise and Vibration Control Engineering—Principles and Applications
,
Wiley
,
New York
, pp.
153
163
.
You do not currently have access to this content.