In this paper, an improved hybrid finite element (FE)-statistical energy analysis (SEA) method is proposed for the mid-frequency vibration of vibro-acoustic systems. Within the framework of the hybrid FE-SEA method, the present method reduces the size of the total dynamic matrix of a vibro-acoustic system by employing dynamic condensation to reduce the order of the dynamic matrix of the acoustic cavity. A fast algorithm is introduced to obtain the dynamic flexibility matrix of the slave degrees-of-freedom (DOFs) of the acoustic cavity FE model, thereby avoiding the direct inverse computation of a large dynamic stiffness matrix at each frequency point of interest. The first numerical example illustrates the validity and efficiency of the present method, while the convergence and accuracy analysis of the proposed method is investigated numerically by the second example.
Issue Section:
Research Papers
References
1.
Ihlenburg
, F.
, Cioranescu
, D.
, and Lloyd
, G.
, 1998
, Finite Element Analysis of Acoustic Scattering
, Springer-Verlag
, New York
.2.
Harari
, I.
, 2006
, “A Survey of Finite Element Methods for Time-Harmonic Acoustics
,” Comp. Methods Appl. Mech. Eng.
, 195
(13–16
), pp. 1594
–1607
. 3.
Li
, E.
, He
, Z. C.
, Xu
, X.
, and Liu
, G. R.
, 2015
, “Hybrid Smoothed Finite Element Method for Acoustic Problems
,” Comp. Methods Appl. Mech. Eng.
, 283
, pp. 664
–688
. 4.
Li
, E.
, He
, Z. C.
, Jiang
, Y.
, and Li
, B.
, 2016
, “3D Mass-Redistributed Finite Element Method in Structural–Acoustic Interaction Problems
,” Acta Mech.
, 227
(3
), pp. 857
–879
. 5.
He
, Z. C.
, Li
, E.
, Liu
, G. R.
, Li
, G. Y.
, and Cheng
, A. G.
, 2016
, “A Mass-Redistributed Finite Element Method (MR-FEM) for Acoustic Problems Using Triangular Mesh
,” J. Comput. Phys.
, 323
, pp. 149
–170
. 6.
Desmet
, W.
, 2002
, “Mid-Frequency Vibro-Acoustic Modelling: Challenges and Potential Solutions
,” Proceedings of 2002 International Conference on Noise and Vibration Engineering
, ISMA, Leuven, Belgium
, pp. 835
–862
.7.
Ladeveze
, P.
, Barbarulo
, A.
, Riou
, H.
, and Kovalevsky
, L.
, 2012
, Mid-Frequency - CAE Methodologies for Mid-Frequency Analysis in Vibration and Acoustics
, Leuven University Press
, Leuven
.8.
He
, Z. C.
, Li
, G. Y.
, Zhong
, Z. H.
, Cheng
, A. G.
, Zhang
, G. Y.
, Li
, E.
, and Liu
, G. R.
, 2012
, “An ES-FEM for Accurate Analysis of 3D Mid-Frequency Acoustics Using Tetrahedron Mesh
,” Comput. Struct.
, 106–107
, pp. 125
–134
. 9.
He
, Z. C.
, Li
, G. Y.
, Li
, E.
, Zhong
, Z. H.
, and Liu
, G. R.
, 2014
, “Mid-Frequency Acoustic Analysis Using Edge-Based Smoothed Tetrahedron Radial point Interpolation Methods
,” Int. J. Comput. Methods
, 11
(5
), 1350103. 10.
Wu
, F.
, He
, Z. C.
, Liu
, G. R.
, Li
, G. Y.
, and Cheng
, A. G.
, 2016
, “A Novel Hybrid ES-FE-SEA for Mid-Frequency Prediction of Transmission Losses in Complex Acoustic Systems
,” Appl. Acoust.
, 111
, pp. 198
–204
. 11.
Shorter
, P. J.
, and Langley
, R. S.
, 2005
, “Vibro-Acoustic Analysis of Complex Systems
,” J. Sound Vib.
, 288
(3
), pp. 669
–699
. 12.
Langley
, R. S.
, and Cordioli
, J. A.
2009
, “Hybrid Deterministic-Statistical Analysis of Vibro-Acoustic Systems With Domain Couplings on Statistical Components
,” J. Sound Vib.
, 321
(3–5
), pp. 893
–912
. 13.
Bathe
, K. J.
, 1996
, Finite Element Procedures
, Prentice Hall
, Upper Saddle River
.14.
Lyon
, R. H.
, and DeJong
, R. G.
, 1995
, Theory and Application of Statistical Energy Analysis
, Butterworth-Heinemann
, Boston
.15.
Shorter
, P. J.
, and Langley
, R. S.
, 2005
, “On the Reciprocity Relationship Between Direct Field Radiation and Diffuse Reverberant Loading
,” J. Acoust. Soc. Am.
, 117
(1
), pp. 85
–95
. 16.
Leung
, A. Y. T.
, 1993
, Dynamic Stiffness and Substructures
, Springer
, London
.17.
Vergote
, K.
, Van Genechten
, B.
, Vandepitte
, D.
, and Desmet
, W.
, 2011
, “On the Analysis of Vibro-Acoustic Systems in the Mid-Frequency Range Using a Hybrid Deterministic-Statistical Approach
,” Comput. Struct.
, 89
(11–12
), pp. 868
–877
. 18.
Desmet
, W.
, 1998
, “A Wave Based Prediction Technique for Coupled Vibro-Acoustic Analysis
,” Ph.D. Thesis
, K. U. Leuven
, Leuven
.19.
Pluymers
, B.
, Van Hal
, B.
, Vandepitte
, D.
, and Desmet
, W.
, 2007
, “Trefftz-Based Methods for Time-Harmonic Acoustics
,” Arch. Comput. Methods Eng.
, 14
(4
), pp. 343
–381
. 20.
Gao
, R.
, Zhang
, Y.
, and Kennedy
, D.
, 2018
, “A Hybrid Boundary Element-Statistical Energy Analysis for the Mid-Frequency Vibration of Vibro-Acoustic Systems
,” Comput. Struct.
, 203
, pp. 34
–42
. 21.
Wu
, T. W.
, 2000
, Boundary Element Acoustics: Fundamentals and Computer Codes
, WIT
, Southampton
.22.
Kuhar
, E. J.
, and Stahle
, C. V.
, 1974
, “Dynamic Transformation Method for Modal Synthesis
,” AIAA J.
12
(5
), pp. 672
–678
. 23.
Atalla
, N.
, and Sgard
, F.
, 2015
, Finite Element and Boundary Methods in Structural Acoustics and Vibration
, CRC Press
, Boca Raton, FL
.24.
“
The Julia Programming Language
,” accessed Mar. 18, 2018, https://julialang.org25.
Cremer
, L.
, Heckl
, M.
, and Petersson
, B. A. T.
, 2005
, Structure-Borne Sound
, 3rd ed., Springer
, Berlin
.Copyright © 2019 by ASME
You do not currently have access to this content.
