Implementation of Different Formulas for Special Green’s Functions in a 3D Half-Space BEM

Thin layers of porous media are widely adopted in sound absorption and noise control applications due to their compact arrangement. Particularly, porous media with low flow resistivity exhibit complex, non-local reaction behavior. Therefore, sound field prediction above these media is computationally challenging. This is due to singularities and branch points in the expression for the reflection coefficient. This paper introduces a framework based on the direct discrete complex image method to analyze the sound field above a rigid-backed, non-locally reacting porous sample. In contrast to traditional complex image applications, the proposed framework avoids the extraction of the quasi-static term and the poles from the reflection coefficient. Instead, the reflection coefficient—including its singularities—is directly approximated in terms of a series of complex exponentials, whose coefficients are determined with the matrix pencil method. This study analyzes the sound field above two test samples made of melamine and rockwool. The sound field computation is efficient and accurate in the near- and in the far-field. Moreover, predicted specific impedances agree well with experimental in situ impedance measurements. The proposed framework serves for more applications including object detection in multilayered porous grounds or sound propagation prediction in layered atmosphere.

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Direct discrete complex image method for sound field evaluation above a non-locally reacting layer

Eser

Gurbuz

Brandão

et al. 2021

The Journal of the Acoustical Society of America

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A Semi-Analytic, Numerically Efficient Model for Low-Frequency Sound Scattering by an Infinite Cylinder Located Near a Boundary

Baynes¹,

Godin

2020

J. Theor. Comp. Acout.

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Scattering of sound by a target can be described as a wave radiated by virtual point sources inside the target. In the Rayleigh scattering regime, the strength of the virtual sources can be calculated analytically. When a target is located close to the ocean surface or another reflecting boundary, reflections of the incident and single-scattered waves from the boundary lead to multiple scattering from the target, with the target being insonified by nearby virtual sources. At low frequencies and for shallow targets, the distance from a virtual source to the target is not necessarily large compared to the acoustic wavelength or the target’s dimensions. Then, multiple orders of scattering make significant contributions and incident wave fields that cannot be approximated as a plane wave. This paper takes advantage of the virtual source concept and recently derived explicit analytic representations of 2D acoustic Green’s functions in unbounded fluids with inclusions of a circular cross-section, to develop a simple, intuitive, and numerically efficient model of multiple scattering. Scattering from soft, hard, and fluid targets is considered. The model is used to study the acoustic field in the vicinity of cylindrical targets near a pressure release surface or a hard bottom.

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Implementation of Different Formulas for Special Green’s Functions in a 3D Half-Space BEM

Cited by 2 publications

References 11 publications

Direct discrete complex image method for sound field evaluation above a non-locally reacting layer

Direct discrete complex image method for sound field evaluation above a non-locally reacting layer

A Semi-Analytic, Numerically Efficient Model for Low-Frequency Sound Scattering by an Infinite Cylinder Located Near a Boundary

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