In this paper, a three-dimensional boundary element method for the eigenanalysis of complex-shaped cavity is presented. A particular integral method is proposed with general absorbing boundary conditions, well suited for determination of the lower modes. In this approach, a polynomial approximation of surface admittance is used with a recent class of compactly supported radial basis function. Two common absorbent models are employed in order to demonstrate the relevance of high-order approximation of the admittance. Resulting eigenproblems of several orders (linear to cubic) are thus performed on basic geometries and a car interior. Results show significant improvements for the computed damped eigenfrequencies and the associated modal reverberation time while using an approximation polynomial matching the surface admittance variation order.
REFERENCES
1.
P. M.
Morse
and R. H.
Bolt
, “Sound waves in rooms
,” Rev. Mod. Phys.
16
, 69
–150
(1944
).2.
S. R.
Bistafa
and J. W.
Morrissey
, “Numerical solutions of the acoustic eigenvalue equation in the rectangular room with arbitrary (uniform) wall impedances
,” J. Sound Vib.
263
, 205
–218
(2003
).3.
A.
Karkkainen
and L.
Karkkainen
, “A sound in a box with different complex impedances on its walls
,” in Proceedings of the Joint Baltic-Nordic Acoustics Meeting
, Mariehamm
, Aland, Finland
(2004
).4.
Y.
Naka
, A. A.
Oberai
, and B. G.
Shinn-Cunningham
, “Acoustic eigenvalues of rectangular rooms with arbitrary wall impedances using the interval newton/generalized bisection method
,” J. Acoust. Soc. Am.
118
, 3662
–3671
(2005
).5.
E. H.
Dowell
, D.
Nardini
, and C. A.
Brebbia
, “Master plan for prediction of vehicle interior noise
,” AIAA J.
18
, 353
–366
(1980
).6.
C. A.
Brebbia
and J.
Dominguez
, Boundary Element, An Introduction Course
(Computational Mechanics Publ.
, Southampton
, 1992
), pp. 131
–146
.7.
A.
Leblanc
, A.
Lavie
, and C.
Vanhille
, “An acoustic resonance study of complex three-dimensional cavities by a particular integral method
,” Acta. Acust. Acust.
91
, 873
–879
(2005
).8.
S.
Ahmad
and P. K.
Banerjee
, “Free vibration analysis using a BEM particular integrals
,” J. Eng. Mech. ASCE
112
, 682
–695
(1986
).9.
P. K.
Banerjee
, S.
Ahmad
, and H. C.
Wang
, “A new BEM formulation for the acoustic eigenfrequency analysis
,” Int. J. Numer. Methods Eng.
26
, 1299
–1309
(1988
).10.
J. F.
Allard
and N.
Atalla
, Propagation of Sound in Porous Media: Modelling Sound Absorbing Materials
(John Wiley and Sons
, New York
, 2009
), 358
pp.11.
A.
Craggs
, “A finite element model for acoustically lined small rooms
,” J. Sound Vib.
108
, 327
–337
(1986
).12.
M. E.
Delany
and E.
Bazley
, “Acoustical properties of fibrous absorbent materials
,” Appl. Acoust.
3
, 105
–116
(1970
).13.
M. D.
Buhmann
, “A new class of radial basis functions with compact support
,” Math. Comput.
70
, 307
–318
(2000
).14.
A.
Leblanc
, A.
Malesys
, and A.
Lavie
, “Compactly supported radial basis functions for the acoustic 3D eigenanalysis using the particular integral method
,” Eng. Anal. Boundary Elem.
36
, 520
–526
(2012
).15.
A. F.
Seybert
, B.
Soenarko
, F. J.
Rizzo
, and D. J.
Shippy
, “An advanced computational method for radiation and scattering of acoustic waves in three dimensions
,” J. Acoust. Soc. Am.
77
, 362
–368
(1985
).16.
O. C.
Zienkiewicz
and R. L.
Taylor
, The Finite Element Method
, 5th ed. (Elsevier
, New York
, 2000
), Vol. 1
, pp. 203
–216
.17.
D.
Nardini
and C. A.
Brebbia
, “A new approach to free vibration analysis using boundary elements
,” Appl. Math. Model.
7
, 157
–162
(1983
).18.
A.
Ali
, C.
Rajakumar
, and S. M.
Yunus
, “On the formulation of the acoustic boundary element eigenvalue problems
,” Int. J. Numer. Methods Eng.
31
, 1272
–1282
(1991
).19.
J.
Du
, W.
Li
, Z.
Liu
, H.
Xu
, and Z.
Ji
, “Acoustic analysis of a rectangular cavity with general impedance boundary conditions
,” J. Acoust. Soc. Am
130
, 807
–817
(2011
).20.
V.
Kehr-Candille
and R.
Ohayon
, “Elasto-acoustic damped vibrations, finite element and modal reduction methods
,” in New Advanced in Computational Structural Mechanics
, edited by P.
Ladevèze
and O. C.
Zienkiewicz
(Elsevier
, New York
, 1992
), pp. 321
–334
.21.
W.
Larbi
, J.-F.
De
, and R.
Ohayon
, “A new finite element method formulation for internal acoustic problems with dissipative walls
,” Int. J. Numer. Methods Eng.
68
, 381
–399
(2006
).© 2012 Acoustical Society of America.
2012
Acoustical Society of America
You do not currently have access to this content.