Multiple scattering by random configurations of circular cylinders: Second-order corrections for the effective wavenumber

Linton, C. M.; Martin, P. A.

doi:10.1121/1.1904270

Cited by 96 publications

(144 citation statements)

References 35 publications

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“…We do not assume any incident forcing; we seek eigensolutions to the problem as we shall see shortly by taking the limit as N → ∞. However, we note that if we had alternatively considered a half-space problem in spirit of, for example [13], the result for the resulting effective wavenumber in the pre-stressed medium would remain unchanged. The terms a j n are coefficients associated with the jth inclusion and nth mode and the coefficients Z n are introduced for convenience as we shall show shortly.…”

Section: Multiple Scatteringmentioning

confidence: 99%

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The effective wavenumber of a pre-stressed nonlinear microvoided composite

Parnell

Abrahams

2011

J. Phys.: Conf. Ser.

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Abstract. By using nonlinear elasticity and a modified version of classical multiple scattering theory we derive an explicit form for the effective wavenumber for horizontally polarized shear (SH) elastic waves propagating through a pre-stressed inhomogeneous material consisting of well-separated cylindrical voids embedded in a neo-Hookean rubber host phase. The resulting effective (incremental) antiplane shear modulus is thus also derived.

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Section: Multiple Scatteringmentioning

confidence: 99%

“…where we were able to take s = 1, j = 2 without loss of generality and we have retained only terms of O((ka) 2 ), employing (13). We recall that…”

Section: Effective Wavenumbermentioning

confidence: 99%

The effective wavenumber of a pre-stressed nonlinear microvoided composite

Parnell

Abrahams

2011

J. Phys.: Conf. Ser.

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“…Extension of Linton's theory Linton et al [17,18] have studied scattering of plane waves incident on finite arrays of identical hard and finite impedance cylinders. Consider an array of N non-identical semi-cylinders.…”

Section: Theoretical Formulationsmentioning

confidence: 99%

Reflection of sound from random distributions of semi-cylinders on a hard plane: models and data

Boulanger

Attenborough

Qin

et al. 2005

J. Phys. D: Appl. Phys.

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A new analytical theory for multiple scattering of cylindrical acoustic waves by an array of finite impedance semi-cylinders embedded in a smooth acoustically hard surface is derived by extending previous results for plane waves [Linton and Martin, J. Acoust. Soc. Am. 117 (6) 3413 -3423 (2005)]. Although the computational demands of the new theory increase as the number of the semi-cylinders in the arrays and/or the frequency increases, the theory offers an improvement on analytical boss theories since the latter (i) are restricted to non-deterministic (infinite) random distributions of semi-cylinders with spacing/radii small compared to the incident wavelength and (ii) are derived only for plane waves. The influence on prediction accuracy of truncation of the infinite system of equations introduced by the new theory is explored empirically. Laboratory measurements have been made over deterministic random arrays of identical varnished wooden semi-cylinders on a glass plate. The agreement between predictions and measured relative Sound Pressure Level spectra is very good both for single deterministic random distributions and for averages representing non-deterministic random distributions. The analytical theory is found to give identical results to a Boundary Element calculation but is much faster to compute.PACS numbers: 43.50.Vt, 43.28.En IntroductionSurface roughness is known to have significant influence on near-grazing sound. One approach to modeling long wavelength sound reflection from randomly rough surfaces considers scattering from idealized roughness elements or 'bosses'. Several measurements have been made of relative sound pressure level (SPL) spectra above rough surfaces, where the roughness height and spacing are small compared to the wavelengths of interest [1][2][3][4][5]. These data have been compared with predictions of models derived by Attenborough and Taherzadeh [1] from a boss theory by Tolstoy [6], [7]. It has been found necessary to adjust the impedance of the scatterers and imbedding plane to obtain good agreement between predictions based on Tolstoy's boss theory and the data. Tolstoy's effective admittance models [6], [7] predict that a surface wave is generated at grazingincidence above a hard rough boundary and that the effective admittance above a hard rough boundary is purely imaginary. However, comparison with data [2] indicates that Tolstoy-based predictions overestimate the surface wave component, especially at grazing incidence, and that it is necessary to include attenuation due to non-specular scatter to obtain a good fit with these data [4]. In other comparisons of predictions and data [5], the assumed location of the effective admittance plane has been adjusted to improve agreement with data at higher frequencies. Poor agreement between laboratory measurements of propagation over rough convex surfaces and

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“…(6) and (7) determine the 3D k eff to order N, while the 2D k eff is usually calculated to order N 2 . [2][3][4]9 It is shown in Sec. 3 that the latter terms can always be ignored for forests which have been considered so far in outdoor propagation.…”

Section: Trunk Layermentioning

confidence: 99%

Effective wavenumbers for sound scattering by trunks, branches, and the canopy in a forest

Ostashev¹,

Wilson²,

Muhlestein³

2017

The Journal of the Acoustical Society of America

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Sound propagation in a forest is often represented as propagation in free space with an effective complex wavenumber, which accounts for scattering and absorption. In this paper, the effective wavenumbers due to sound scattering by trunks, large branches, and the canopy are determined and analyzed based on three-dimensional multiple scattering theory. Trunks and branches are modeled as vertical and slanted finite cylinders, while the canopy is modeled by diffuse scatterers. The results are compared with two-dimensional effective wavenumbers previously used in the literature, which were obtained by approximating the trunk layer as infinite vertical cylinders.

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Multiple scattering by random configurations of circular cylinders: Second-order corrections for the effective wavenumber

Cited by 96 publications

References 35 publications

The effective wavenumber of a pre-stressed nonlinear microvoided composite

The effective wavenumber of a pre-stressed nonlinear microvoided composite

Reflection of sound from random distributions of semi-cylinders on a hard plane: models and data

Effective wavenumbers for sound scattering by trunks, branches, and the canopy in a forest

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