An interpolated time-domain equivalent source method for modeling transient acoustic radiation over a mass-like plane based on the transient half-space Green’s function

Pan, Siwei; Jiang, Weikang; Xiang, Shang; Liu, Xiujuan

doi:10.1016/j.wavemoti.2014.07.010

Cited by 16 publications

(4 citation statements)

References 34 publications

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“…Recently, the time-domain ESM has been used in sound visualization and near-field acoustical holography. [87][88][89][90][91][92][93] The time-domain ESM was only used for the rigid boundary condition. However, the absorbing boundary condition in the presence of flow in the time domain 94 is available.…”

Section: Equivalent Source Methodsmentioning

confidence: 99%

Review: The Use of Equivalent Source Method in Computational Acoustics

Lee

2017

J. Comp. Acous.

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This paper reviews the equivalent source method (ESM), an attractive alternative to the standard boundary element method (BEM). The ESM has been developed under different names: method of fundamental solutions, wave superposition method, equivalent source method, etc. However, regardless of the method name, the basic concept is very similar; that is to use auxiliary points called equivalent sources to reconstruct the acoustic pressure for radiation or scattering problems. The strength of the equivalent sources are then determined via various approaches such that the boundary conditions on the boundary surface are satisfied. This paper reviews several frequencydomain and time-domain ESMs. There are several distinct advantages in these types of methods: (1) the method is a meshless approach so that it is easy and simple to implement; (2) it does not have a numerical singularity problem that occurs in the BEM; (3) the number of equivalent sources can be fewer than the number of surface collocation points so that the matrix size is reduced and a fast computation is achieved for large problems. The main issue of the ESM is that there is no rule to find out the optimal number and position of equivalent sources. In addition, the ESM suffers from the numerical instability that is associated with the ill-conditioned matrix. Some guidelines have been suggested in terms of finding the number and position of the sources, and several numerical techniques have been developed to resolve the numerical instability. This paper reviews the common theories, numerical issues and challenges of the ESM, and it summarizes recent developments and applications of the ESM to aircraft noise.

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Section: Equivalent Source Methodsmentioning

confidence: 99%

Review: The Use of Equivalent Source Method in Computational Acoustics

Lee

2017

J. Comp. Acous.

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“…Bi等 [9−11] 参照等效源法, 使用一组半空间格林函数的线性叠加来表述全息测量声压, 通过求解半空间格林函数系数, 实现半空间声学量的重构. Pan等 [12,13] 将时域的半空间格林函数引入到等效源法中, 对半空间瞬态声场进行了重构. 上述方法将边界阻抗作为参量分别引入傅里叶声学法、逆边界元法和等效源法的数学模型, 建立半空间声场的数学模型和相应的声场重构算法.…”

Section: 立半空间中场点声学量与声源表面声学量之间的unclassified

Reconstruction of half-space boundary impedance and sound source direct radiation based on reflection coefficient estimation

Zhou¹,

Lu²,

Xiangle³

et al. 2022

Acta Phys. Sin.

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When implementing the reconstruction of the acoustic field directly radiated from a source located in a half-space, the half-space basis functions with boundary impedance as a parameter, need to be formulated. And the boundary impedance is usually obtained via in situ acoustic impedance measurement techniques. The reconstruction method based on the expansion in half-space spherical wave basis functions, uses a hologram surface and a single reference microphone placed in the near-field to collect acoustic pressures. The acoustic pressure at the reference microphone is reconstructed firstly and the error of the reconstructed pressure relative to the measured pressure is then calculated. The acoustic pressure reflection coefficient corresponding to the minimum error is chosen as the estimation of the reflection coefficient at the measurement points. Thus, this method is applicable to reconstruct the directly radiated acoustic pressures without the knowledge of boundary impedance, free from the in situ acoustic impedance measurement techniques necessary for conventional methods. The purpose of this thesis is to discuss the various parameters affecting the accuracy of reconstruction. Moreover, the boundary impedance is reconstructed based on the estimation of the reflection coefficient, so that an acoustic impedance measurement technique implemented via the near-field acoustical holography is proposed. By taking the spherical source as an example, numerical simulations are conducted to verify the proposed method in reconstruction of the boundary impedance and the directly radiated acoustic pressures. The impacts of reference microphone coordinate, the effective flow resistivity of the boundary, and the rate of decrease of porosity with depth of the boundary on the accuracy of reconstruction are quantitatively analyzed.

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“…The main idea of ESM is that the sound field generated by a source is replaced by a set of monopole sources distributed on a surface at a certain distance from the surface of the radiating structure, and the source intensity of the equivalent source can be obtained by matching the normal vibration velocity of the surface of the source. Compare with other methods, such as the analytical method [9][10][11], finite element method [12][13][14], boundary element method [15][16][17], and ESM [18][19][20][21] are more suitable for reconstructing the radiated sound field of arbitrarily shaped sources and can require less computational effort and avoid complex interpolation operations and singular integration processing. Many scholars have conducted a series of studies on ESM to improve the resolution of sound sources and the accuracy of sound field reconstruction.…”

Section: Introductionmentioning

confidence: 99%

Application of equivalent source intensity density interpolation in near-field acoustic holography

Gao

Yang

et al. 2023

Meas. Sci. Technol.

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The spatial resolution of near-field acoustic holography based on the equivalent source method (ESM) is closely related to the number of measurement points, the higher the number of measurement points, the higher the resolution. However, the number of measurement points in the actual measurement cannot be increased infinitely. To solve the contradiction between the resolution and the number of measurement points, this paper proposes an equivalent source density interpolation method (ESDIM). First, the equivalent source intensity is obtained using the sound pressure measured by the array element and the Green function, and the equivalent source intensity density is obtained based on the equivalent source intensity and grid area. Second, the Hermite interpolation function was used to obtain the interpolated equivalent source intensity density. However, as the number of interpolated grids increased, the resolution, computation, and running time of ESDIM increased, and the number of subdivided grids per unit grid was 9-25 in this study. Finally, the sound field was reconstructed based on the obtained interpolated equivalent source intensity and Green transfer function, and the reconstruction accuracies of ESDIM and ESM were compared and analyzed. The simulation and experimental data processing results showed that the resolution of the equivalent source intensity density interpolation method was higher than that of the equivalent source method.

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An interpolated time-domain equivalent source method for modeling transient acoustic radiation over a mass-like plane based on the transient half-space Green’s function

Cited by 16 publications

References 34 publications

Review: The Use of Equivalent Source Method in Computational Acoustics

Review: The Use of Equivalent Source Method in Computational Acoustics

Reconstruction of half-space boundary impedance and sound source direct radiation based on reflection coefficient estimation

Application of equivalent source intensity density interpolation in near-field acoustic holography

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