Resonant elastic scattering by a finite number of cylindrical cavities in an elastic matrix

Robert, Sébastien; Conoir, Jean-Marc; Franklin, Hervé; Luppé, Francine

doi:10.1016/j.wavemoti.2004.03.003

Cited by 15 publications

(7 citation statements)

References 25 publications

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“… Waterman and Truell [1961] have proposed an effective medium theory taking multiple scattering into account. This model has been applied to the problem of an elastic wave scattered by a finite number of inclusions inside a homogeneous matrix [ McClements and Povey , 1989; Anson and Chivers , 1993; Robert et al , 2004]. This model also considers the case of spherical scatterers embedded in a fluid matrix.…”

Section: Effective Medium Theoriesmentioning

confidence: 99%

Multiscale analysis of waves reflected by granular media: Acoustic experiments on glass beads and effective medium theories

Gonidec

Gibert

2007

J. Geophys. Res.

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To cite this version:Yves Le Gonidec, Dominique Gibert. Multiscale analysis of waves reflected by granular media: Acoustic experiments on glass beads and effective medium theories. [1] The wavelet response is a multiscale method based on the continuous wavelet transform. We use it to characterize the acoustic reflectivity of a layer of glass beads with diameter d = 1 mm randomly arranged in water. The volumetric concentration is f ' 63% of spherical inclusions. The wavelet response is measured over a large frequency range (100 kHz f 5 MHz) where five different acoustic regimes are identified on the basis of scattering phenomena. A strong decrease in the reflectivity occurs when the wavelength of the incident wave is twice the bead diameter, a situation where lateral scattering is dominant. The energy ratio of the ballistic and the coda parts of the wavelet response reveals a clear transition from a ballistic propagation regime to a diffusion regime where multiple scattering occurs. The experimental data are explained with an effective medium theory approach: the reflectivity data in the low-frequency domain of the spanned frequency range are correctly reproduced with quasi-static models. For higher frequencies, more sophisticated models accounting for multiple scattering must be used. The high-frequency part of the experimental reflectivity curve may be explained by strong multiple scattering at the top of the glass beads located at the surface of the layer and corresponds to the optical geometric limit.Citation: Le Gonidec, Y., and D. Gibert (2007), Multiscale analysis of waves reflected by granular media: Acoustic experiments on glass beads and effective medium theories,

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Section: Effective Medium Theoriesmentioning

confidence: 99%

Multiscale analysis of waves reflected by granular media: Acoustic experiments on glass beads and effective medium theories

Gonidec

Gibert

2007

J. Geophys. Res.

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“…T(j À 1) when the incident wave propagates in the opposite direction [see Eqs (11)- (13)]. Between the set of (j À 1) rows and the jth row separated by the distance D jÀ1 , there exist multiple reflections and transmissions.…”

Section: Engineering Pass Bands and Stop Bandsmentioning

confidence: 99%

“…The same method has been used for fluid cavities in an elastic matrix. 13 The first part of the method is devoted to a multiple scattering calculation between the scatterers forming one row and then allows us to find the scattering properties of this row, e.g., the reflection and transmission coefficients. The second part considers that the slab is made up of a sequence of periodically or not arranged rows, each one with known reflection and transmission coefficients.…”

Section: Introductionmentioning

confidence: 99%

Effects of periodicity perturbations on the transmission by underwater phononic crystals

Zong

Franklin

Lenoir

et al. 2012

The Journal of the Acoustical Society of America

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The effects of periodicity perturbations in underwater phononic crystal layers composed of noninterpenetrating rows of identical shells are investigated. The results for one row are obtained by using a multiple scattering method between shells. Then, taking into account the multiple reflections and transmissions between two adjacent rows, a Debye series method is used to calculate the reflection and transmission coefficients by a finite number of rows. The paper focuses on three kinds of perturbations: (i) variation of the inner radius of shells from row to row, (ii) increase in the spacing from row to row and of the number of rows, and (iii) substitution of simple steel rows by steel-polyethylene bilayers. It is shown by studying the transmission coefficient that the case (i) permits the insertion of narrow pass bands in the stop band while the two other cases (ii) and (iii) widen the stop band. The study intends to model simple underwater acoustic filters.

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“…More recently, Huang and Gaunaurd [21,22] denoted a solution of scattering of coherent acoustic waves by two spherical shells. Robert et al [23] proposed a way of solving the scattering problems by finite cylindrical cavities. Le Bas et al [24]studied the multiple scattering and fission phenomena by multishell in water.…”

Section: Introductionmentioning

confidence: 99%

Ground Vibration Isolation of Multiple Scattering by Using Rows of Tubular Piles as Barriers

Sun

Guo-qian

Xia

et al. 2014

Shock and Vibration

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A new formal solution for the multiple scattering of plane harmonic waves by a group of arbitrary configuration tubular piles in an elastic total space is derived. Each order of scattering satisfies prescribed boundary conditions at the interface of tubular piles, which is delivered as the sum of incident and scattering waves. The first order performs the scattering wave by each scattered pile and the subsequent orders resulted from the excitation of each pile of first order of scattering from the remaining tubular piles. Advanced scattering orders can be regarded as the same manners. Several series of scattering coefficients are figured out with the aids of addition theorem so that the exact steady-state solution for the scattered displacement and stress is obtained. Particularly, when internal diameter of tubular piles tends to be infinitely small, it degenerates to a solid pile problem. By imposing the normalized displacement amplitudes and transmissibility indices, the influences of specific parameters such as scattering orders, internal and external diameter ratio of piles, pile material rigidity, position and distances between tubular pile and pile rows, and pile numbers are discussed. Certain recommended conclusions have been drawn as the guidelines of practical engineering design for discontinuous barrier of tubular piles.

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Resonant elastic scattering by a finite number of cylindrical cavities in an elastic matrix

Cited by 15 publications

References 25 publications

Multiscale analysis of waves reflected by granular media: Acoustic experiments on glass beads and effective medium theories

Multiscale analysis of waves reflected by granular media: Acoustic experiments on glass beads and effective medium theories

Effects of periodicity perturbations on the transmission by underwater phononic crystals

Ground Vibration Isolation of Multiple Scattering by Using Rows of Tubular Piles as Barriers

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