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Research Papers

An Inverse Direct Time Domain Boundary Element Method for the Reconstruction of Transient Acoustic Field

[+] Author and Article Information
Yang Zhang

Institute of Sound and Vibration Research,
Hefei University of Technology,
193 Tunxi Road,
Hefei 230009, China
e-mail: 2012110154@mail.hfut.edu.cn

Xiao-Zheng Zhang

Institute of Sound and Vibration Research,
Hefei University of Technology,
193 Tunxi Road,
Hefei 230009, China
e-mail: xzhengzhang@hfut.edu.cn

Chuan-Xing Bi

Institute of Sound and Vibration Research,
Hefei University of Technology,
193 Tunxi Road,
Hefei 230009, China
e-mail: cxbi@hfut.edu.cn

Yong-Bin Zhang

Institute of Sound and Vibration Research,
Hefei University of Technology,
193 Tunxi Road,
Hefei 230009, China
e-mail: ybzhang@hfut.edu.cn

1Corresponding author.

Contributed by the Noise Control and Acoustics Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received August 3, 2016; final manuscript received November 25, 2016; published online February 20, 2017. Assoc. Editor: Theodore Farabee.

J. Vib. Acoust 139(2), 021013 (Feb 20, 2017) (8 pages) Paper No: VIB-16-1386; doi: 10.1115/1.4035381 History: Received August 03, 2016; Revised November 25, 2016

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.

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Figures

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Fig. 1

Geometry of radiation problem

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Fig. 2

Schematic view of the minimum and maximum distances between source point and field point

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Fig. 3

Time axes for DTBEM. There is a retarded time between source surface and receiver surface.

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Fig. 4

Time axes for IDTBEM. New initial time is defined on the measurement surface (receiver surface in the DTBEM).

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Fig. 5

Geometry of the impulsively accelerated sphere and the measurement surface H. The origin of the spherical coordinate system O(r,θ,φ) is located at the center of the sphere. The radius of the sphere is 0.1 m. The source surface Γ is the surface of the sphere. The measurement surface H is a spherical surface whose radius is 0.1181 m.

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Fig. 6

Time domain waveform comparisons of reconstructed pressures (dotted dot line) without using regularization and analytical pressures (solid line) at (a) point (0.1 m, 0 rad, 0 rad) and (b) point (0.1 m, 0.5416 rad, 0.7854 rad)

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Fig. 7

Time domain waveform comparisons of reconstructed pressures (dotted solid line) with the TSVD and analytical pressures (solid line) at (a) point (0.1 m, 0 rad, 0 rad) and (b) point (0.1 m, 0.5416 rad, 0.7854 rad)

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Fig. 8

Spatial distributions of analytical pressures at t=0.39969 ms (a) and t=0.53292 ms (b) and reconstructed pressures at t=0.39969 ms (c) and t=0.53292 ms (d) on the source surface

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Fig. 9

Geometry of the vibrating cylinder and the measurement surface H. The origin of the Cartesian coordinate system O(x,y,z) is located at the center of the cylinder. The diameter of the cylinder is dc=0.064 m, and the length of the cylinder is hc=0.02 m. The source surface Γ is the surface of the cylinder. The diameter and length of the measurement surface H are dm=0.0789 m and hm=0.0349 m, respectively.

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Fig. 10

Time domain waveform comparisons of reconstructed pressures (dotted solid line) and analytical pressures (solid line) at (a) point (0.0288, 0.01, −0.0139) m and (b) point (−0.0112, 0.01, −0.0178) m

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Fig. 11

Spatial distributions of analytical pressures at t=1.4616 ms (a) and t=2.0029 ms (b) and reconstructed pressures at t=1.4616 ms (c) and t=2.0029 ms (d) on the source surface

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Fig. 12

The simplified car model and the mesh of the surface with 1155 elements and 1139 nodes. The origin of the Cartesian coordinate system O(x,y,z) is located at the geometrical center of the car model. The size of the car is 5.8×2.4×1.5 m3. The marked patches indicate the location where the flux initiated.

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Fig. 13

Time domain waveform comparisons of reconstructed pressures (dotted solid line) and analytical pressures (solid line) at (a) point (1.1152, −0.7789, −0.2665) m and (b) point (0.3186, 1.203, 0.6122) m

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Fig. 14

Spatial distributions of analytical pressures at t=45.464 ms (a) and t=53.884 ms (b) and reconstructed pressures at t=45.464 ms (c) and t=53.884 ms (d) on the source surface

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