Upward refraction of sound propagating outdoors by a graded index sonic crystal noise barrier

Aa, Bart van der; Forssén, Jens

doi:10.1016/j.apacoust.2012.06.012

Cited by 13 publications

(3 citation statements)

References 18 publications

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“…A rigid boundary can be characterised by a disappearing particle velocity normal to the boundary, which is equivalent to a vanishing pressure gradient, that is satisfying the Neumann condition. An acceptable example can be the ground during outdoor sound propagation (10,11). A rigid boundary is also known as 'sound-hard' (1, p. 13) and has the plane-wave pressure reflection coefficient of +1.…”

Section: Image Condition: Rigid Interfacementioning

confidence: 99%

“…Since the inception of sonic crystals using horizontal circular cylinders as a potential tool for outdoor noise mitigation, multiple scattering works have been carried out in conjunction with the method of images due to the inevitable presence of outdoor ground (9)(10)(11). Underwater sound scattering underneath the free surface has also been analysed with similar approaches (12,13).…”

Section: Introductionmentioning

confidence: 99%

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Image conditions for polar and cylindrical coordinate separation-of-variables acoustic multiple scattering models with perfectly reflecting flat boundaries

Shin

2018

The Quarterly Journal of Mechanics and Applied Mathematics

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This article addresses efficient implementation of the method of images for acoustic multiple scattering models (MSM) with perfectly reflecting flat boundaries. Time-harmonic problems are first solved in the polar coordinate system for circular scatterers; then the models are extended to the cylindrical coordinate system with (semi-)infinitely long circular cylinders. The MSM in this article is based on the method of separation of variables and Graf's addition theorem. Derivations are provided for 'image conditions' which relate the unknown coefficients of outgoing waves from image scatterers with those of real counterparts. The method of images is applied to wedgeshaped domains with apex angles of π/n rad for a positive integer n. Image conditions make the MSM numerically more efficient: the system of linear equations for unknown coefficients is formulated 2n times faster; its memory requirements are reduced by 4n 2 times for direct solvers. The proposed model is applied to a benchmark wedge in ocean environment with n = 64. Good agreement is observed between the MSM with image conditions and the boundary element method. Furthermore, half-and quarter-space measurements in an anechoic chamber are in accordance with the correct use of image conditions. Incorrect image conditions reported elsewhere for polar coordinates are also discussed.

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Section: Image Condition: Rigid Interfacementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Image conditions for polar and cylindrical coordinate separation-of-variables acoustic multiple scattering models with perfectly reflecting flat boundaries

Shin

2018

The Quarterly Journal of Mechanics and Applied Mathematics

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“…the initial flux of energy is partially redirected by 90 • . The effect of redirection of acoustic energy was recently predicted not only for periodic systems of scatterers [16,19,22] but also for a narrow fluid channel in a solid elastic plate [23,24].…”

Section: Introductionmentioning

confidence: 99%

Redirection and Splitting of Sound Waves by a Periodic Chain of Thin Perforated Cylindrical Shells

et al. 2017

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Scattering of sound by finite and infinite chains of equally spaced perforated metallic cylindrical shells in an ideal (inviscid) and viscous fluid is theoretically studied using rigorous analytical and numerical approaches. Due to perforations, a chain of thin shells is practically transparent for sound within a wide range of frequencies. It is shown that strong scattering and redirection of sound by 90 • may occur only for a discrete set of frequencies (Wood's anomalies) where the leaky eigenmodes are excited. The spectrum of eigenmodes consists of antisymmetric and symmetric branches with normal and anomalous dispersion, respectively. The antisymmetric eigenmode turns out to be a deaf mode since it cannot be excited at normal incidence. However, at slightly oblique incidence both modes can be excited at different but close frequencies. The symmetric mode, due to its anomalous dispersion, scatters sound in the "wrong" direction, thus allowing splitting of the incoming signal containing two harmonics into two beams propagating along the chain in the opposite directions. Calculations are presented for aluminum shells in viscous air where the effects of anomalous scattering, redirection, and signal splitting are well manifested.

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Shape-optimal design of graded index sonic crystal formations using natural cubic splines

Forssén

2014

Applied Acoustics

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Upward refraction of sound propagating outdoors by a graded index sonic crystal noise barrier

Cited by 13 publications

References 18 publications

Image conditions for polar and cylindrical coordinate separation-of-variables acoustic multiple scattering models with perfectly reflecting flat boundaries

Image conditions for polar and cylindrical coordinate separation-of-variables acoustic multiple scattering models with perfectly reflecting flat boundaries

Redirection and Splitting of Sound Waves by a Periodic Chain of Thin Perforated Cylindrical Shells

Shape-optimal design of graded index sonic crystal formations using natural cubic splines

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