An inverse direct time domain boundary element method (IDTBEM) is proposed for the reconstruction of transient acoustic field radiated by arbitrarily shaped sources. The method is based on the theory of direct time domain boundary element method (DTBEM), which is free from the calculation of hypersingular integrals, and thus, its reconstruction process is relatively simple and easy to implement. However, the formulations of DTBEM cannot be used directly for the reconstruction of transient acoustic field, and therefore, new formulations with a modified time axis are derived. With these new formulations, a linear system of equations is formed and the reconstruction is performed in a marching-on-time (MOT) way. Meanwhile, to deal with the ill-posedness involved in the inverse process, the truncated singular value decomposition (TSVD) is employed. Numerical simulations with three examples of a sphere, a cylinder, and a simplified car model are carried out to verify the validity of IDTBEM, and the results demonstrate that the IDTBEM is effective in reconstructing the transient acoustic fields radiated by arbitrarily shaped sources in both time and space domains.
Issue Section:
Research Papers
References
1.
Williams
, E. G.
, and Maynard
, J. D.
, 1980
, “Holographic Imaging Without the Wavelength Resolution Limit
,” Phys. Rev. Lett.
, 45
(7
), pp. 554
–557
.2.
Williams
, E. G.
, Maynard
, J. D.
, and Skudrzky
, E.
, 1980
, “Sound Source Reconstructions Using a Microphone Array
,” J. Acoust. Soc. Am.
, 68
(1
), pp. 340
–344
.3.
Williams
, E. G.
, 1999
, Fourier Acoustics: Sound Radiation and Nearfield Acoustical Holography
, Academic Press
, London
, Chap. 3.4.
Gardner
, B. K.
, and Bernhard
, R. J.
, 1988
, “A Noise Source Identification Technique Using an Inverse Helmholtz Integral Equation Method
,” ASME J. Vib. Acoust. Stress Reliab. Des.
, 110
(1
), pp. 84
–90
.5.
Veronesi
, W. A.
, and Maynard
, J. D.
, 1989
, “Digital Holographic Reconstruction of Sources With Arbitrarily Shaped Surfaces
,” J. Acoust. Soc. Am.
, 85
(2
), pp. 588
–598
.6.
Kim
, B. K.
, and Ih
, J. G.
, 1996
, “On the Reconstruction of Vibro-Acoustic Field Over the Surface Enclosing an Interior Space Using the Boundary Element Method
,” J. Acoust. Soc. Am.
, 100
(5
), pp. 3030
–3016
.7.
Kim
, Y. K.
, and Kim
, Y. H.
, 1999
, “Holographic Reconstruction of Active Sources and Surface Admittance in an Enclosure
,” J. Acoust. Soc. Am.
, 105
(4
), pp. 2377
–2383
.8.
Kim
, G. T.
, and Lee
, B. T.
, 1990
, “3-D Sound Source Reconstruction and Field Reproduction Using the Helmholtz Integral Equation
,” J. Sound Vib.
, 136
(2
), pp. 245
–261
.9.
Bai
, M. R.
, 1992
, “Application of BEM (Boundary Element Method)-Based Acoustic Holography to Radiation Analysis of Sound Sources With Arbitrarily Shaped Geometries
,” J. Acoust. Soc. Am.
, 92
(1
), pp. 533
–548
.10.
Chappell
, D. J.
, and Harris
, P. J.
, 2009
, “A Burton-Miller Inverse Boundary Element Method for Near-Field Acoustic Holography
,” J. Acoust. Soc. Am.
, 126
(1
), pp. 149
–157
.11.
Sarkissian
, A.
, Gaumond
, C. F.
, Williams
, E. G.
, and Houston
, B. H.
, 1993
, “Reconstruction of the Acoustic Field Over a Limited Surface Area on a Vibrating Cylinder
,” J. Acoust. Soc. Am.
, 93
(1
), pp. 48
–54
.12.
Valdivia
, N. P.
, Williams
, E. G.
, and Herdic
, P. C.
, 2008
, “Approximations of Inverse Boundary Element Methods With Partial Measurements of the Pressure Field
,” J. Acoust. Soc. Am.
, 123
(1
), pp. 109
–120
.13.
Wu
, S. F.
, and Zhao
, X.
, 2002
, “Combined Helmholtz Equation-Least Squares Method for Reconstructing Acoustic Radiation From Arbitrarily Shaped Objects
,” J. Acoust. Soc. Am.
, 112
(1
), pp. 179
–188
.14.
Wu
, S. F.
, 2004
, “Hybrid Near-Field Acoustic Holography
,” J. Acoust. Soc. Am.
, 115
(1
), pp. 207
–217
.15.
Langrenne
, C.
, Melon
, M.
, and Garcia
, A.
, 2007
, “Boundary Element Method for the Acoustic Characterization of a Machine in Bounded Noisy Environment
,” J. Acoust. Soc. Am.
, 121
(5
), pp. 2750
–2757
.16.
Langrenne
, C.
, Melon
, M.
, and Garcia
, A.
, 2009
, “Measurement of Confined Acoustic Sources Using Near-Field Acoustic Holography
,” J. Acoust. Soc. Am.
, 126
(3
), pp. 1250
–1256
.17.
Valdivia
, N.
, and Williams
, E. G.
, 2004
, “Implicit Methods of Solution to Integral Formulations in Boundary Element Method Based Nearfield Acoustic Holography
,” J. Acoust. Soc. Am.
, 116
(3
), pp. 1559
–1572
.18.
Zhang
, Z.
, Vlahopoulos
, N.
, Allen
, T.
, and Zhang
, K. Y.
, 2001
, “A Source Reconstruction Process Based on an Indirect Variational Boundary Element Formulation
,” Eng. Anal. Boundary Elem.
, 25
(2
), pp. 93
–114
.19.
Vlahopoulos
, N.
, and Raveerdra
, S. T.
, 1998
, “Formulation, Implementation and Validation of Multiple Connection and Free Edge Constraints in an Indirect Boundary Element Formulation
,” J. Sound Vib.
, 210
(1
), pp. 137
–152
.20.
Friedman
, M. B.
, and Shaw
, R. P.
, 1962
, “Diffraction of Pulses by Cylindrical Obstacles of Arbitrary Cross Section
,” ASME J. Appl. Mech.
, 29
(1
), pp. 40
–46
.21.
Mitzner
, K. M.
, 1967
, “Numerical Solution for Transient Scattering From a Hard Surface of Arbitrary Shape-Retarded Potential Technique
,” J. Acoust. Soc. Am.
, 42
(2
), pp. 391
–397
.22.
Ding
, Y.
, Forestier
, A.
, and Duong
, T. H.
, 1989
, “A Galerkin Scheme for the Time Domain Integral Equation of Acoustic Scattering From a Hard Surface
,” J. Acoust. Soc. Am.
, 86
(4
), pp. 1566
–1572
.23.
Bluck
, M. J.
, and Walker
, S. P.
, 1996
, “Analysis of Three-Dimensional Transient Acoustic Wave Propagation Using the Boundary Integral Equation Method
,” Int. J. Numer. Methods Eng.
, 39
(8
), pp. 1419
–1431
.24.
Chappell
, D. J.
, 2011
, “Convolution Quadrature Galerkin Boundary Element Method for the Wave Equation With Reduced Quadrature Weight Computation
,” IMA J. Numer. Anal.
, 31
(2
), pp. 640
–666
.25.
Rynne
, B. P.
, 1985
, “Stability and Convergence of Time Marching Methods in Scattering Problems
,” IMA J. Appl. Math.
, 35
(3
), pp. 297
–310
.26.
Ergin
, A. A.
, Shanker
, B.
, and Michielssen
, E.
, 1999
, “Analysis of Transient Wave Scattering From Rigid Bodies Using a Burton–Miller Approach
,” J. Acoust. Soc. Am.
, 106
(5
), pp. 2396
–2404
.27.
Chappell
, D. J.
, Harris
, P. J.
, Henwood
, D.
, and Chakrabarti
, R.
, 2006
, “A Stable Boundary Element Method for Modeling Transient Acoustic Radiation
,” J. Acoust. Soc. Am.
, 120
(1
), pp. 76
–80
.28.
Jang
, H. W.
, and Ih
, J. G.
, 2012
, “Stabilization of Time Domain Acoustic Boundary Element Method for the Interior Problem With Impedance Boundary Conditions
,” J. Acoust. Soc. Am.
, 131
(4
), pp. 2742
–2752
.29.
Jang
, H. W.
, and Ih
, J. G.
, 2012
, “Stabilization of Time Domain Acoustic Boundary Element Method for the Exterior Problem Avoiding the Nonuniqueness
,” J. Acoust. Soc. Am.
, 133
(3
), pp. 1237
–1244
.30.
Troclet
, B.
, Alestra
, S.
, Srithammavanh
, V.
, and Terrasse
, I.
, 2011
, “A Time Domain Inverse Method for Identification of Random Acoustic Sources at Launch Vehicle Lift-Off
,” ASME J. Vib. Acoust.
, 133
(2), pp. 1
–11
.31.
Mansur
, W. J.
, 1983
, “A Time-Stepping Technique to Solve Wave Propagation Problems Using the Boundary Element Method
,” Ph.D. thesis
, Southampton University, Southampton, UK.32.
Hald
, J.
, 2001
, “Time Domain Acoustical Holography and Its Applications
,” J. Sound Vib.
, 35
(2), pp. 16
–24
.33.
Rochefoucauld
, O. D. L.
, Melon
, M.
, and Garcia
, A.
, 2004
, “Time Domain Holography: Forward Projection of Simulated and Measured Sound Pressure Fields
,” J. Acoust. Soc. Am.
, 116
(1
), pp. 142
–153
.34.
Blais
, J.-F.
, and Ross
, A.
, 2009
, “Forward Projection of Transient Sound Pressure Fields Radiated by Impacted Plates Using Numerical Laplace Transform
,” J. Acoust. Soc. Am.
, 125
(5
), pp. 3120
–3128
.35.
Deblauwe
, F.
, Leuridan
, J.
, Chauray
, J. L.
, and Béguet
, B.
, 1999
, “Acoustic Holography in Transient Conditions
,” Sixth International Congress on Sound and Vibration
, Copenhagen, Denmark, pp. 899
–906
.36.
Grulier
, V.
, Paillasseur
, S.
, Thomas
, J.-H.
, and Pascal
, J.-C.
, 2009
, “Forward Propagation of Time Evolving Acoustic Pressure: Formulation and Investigation of the Impulse Response in Time-Wavenumber Domain
,” J. Acoust. Soc. Am.
, 126
(5
), pp. 2367
–2378
.37.
Thomas
, J.-H.
, Grulier
, V.
, Paillasseur
, S.
, Pascal
, J.-C.
, and Le Roux
, J.-C.
, 2010
, “Real-Time Nearfield Acoustical Holography for Continuously Visualizing Nonstationary Acoustic Fields
,” J. Acoust. Soc. Am.
, 128
(6
), pp. 3554
–3567
.38.
Wu
, S. F.
, Lu
, H.
, and Bajwa
, M. S.
, 2004
, “Reconstruction of Transient Acoustic Radiation From a Sphere
,” J. Acoust. Soc. Am.
, 117
(4
), pp. 2065
–2077
.39.
Wu
, S. F.
, 2014
, “Reconstructing Transient Acoustic Radiation From an Arbitrary Object With a Uniform Surface Velocity Distribution
,” J. Acoust. Soc. Am.
, 136
(2
), pp. 514
–524
.40.
Zhang
, X. Z.
, Bi
, C. X.
, Zhang
, Y. B.
, and Xu
, L.
, 2011
, “Transient Nearfield Acoustic Holography Based on an Interpolated Time-Domain Equivalent Source Method
,” J. Acoust. Soc. Am.
, 130
(3
), pp. 1430
–1440
.41.
Bi
, C. X.
, Geng
, L.
, and Zhang
, X. Z.
, 2013
, “Cubic Spline Interpolation-Based Time-Domain Equivalent Source Method for Modeling Transient Acoustic Radiation
,” J. Sound Vib.
, 332
(22
), pp. 5939
–5952
.42.
Rizos
, D. C.
, and Zhou
, S.
, 2006
, “An Advanced Direct Time Domain BEM for 3-D Wave Propagation in Acoustic Media
,” J. Sound Vib.
, 293
(1
), pp. 196
–212
.43.
Duong
, T. H.
, Ludwig
, B.
, and Terrasse
, I.
, 2003
, “A Galerkin BEM for Transient Acoustic Scattering by an Absorbing Obstacle
,” Int. J. Numer. Methods Eng.
, 57
(13
), pp. 1845
–1882
.44.
Williams
, E. G.
, Houston
, B. H.
, and Herdic
, P. C.
, 2003
, “Fast Fourier Transform and Singular Value Decomposition Formulations for Patch Nearfield Acoustical Holography
,” J. Acoust. Soc. Am.
, 114
(3
), pp. 1322
–1333
.45.
Nelson
, P. A.
, and Yoon
, S. H.
, 2000
, “Estimation of Acoustic Source Strength by Inverse Methods—Part I: Conditioning of the Inverse Problem
,” J. Sound Vib.
, 233
(4
), pp. 643
–668
.46.
Nelson
, P. A.
, and Yoon
, S. H.
, 2000
, “Estimation of Acoustic Source Strength by Inverse Methods—Part II: Experimental Investigation of Methods for Choosing Regularization Parameters
,” J. Sound Vib.
, 233
(4
), pp. 669
–705
.47.
Wu
, S. F.
, 1993
, “Transient Sound Radiation From Impulsively Accelerated Bodies
,” J. Acoust. Soc. Am.
, 94
(1
), pp. 542
–553
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