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Research Papers

A Mode-Resolved Continuum Mechanics Model of Acoustic Wave Scattering From Embedded Cylinders

[+] Author and Article Information
Vineet Unni

Department of Mechanical Engineering,
University of Delaware,
Newark, DE 19716
e-mail: vineetu@udel.edu

Joseph P. Feser

Department of Mechanical Engineering,
University of Delaware,
Newark, DE 19716
e-mail: jpfeser@udel.edu

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received March 30, 2018; final manuscript received July 19, 2018; published online September 10, 2018. Assoc. Editor: Stefano Gonella.

J. Vib. Acoust 141(1), 011015 (Sep 10, 2018) (9 pages) Paper No: VIB-18-1133; doi: 10.1115/1.4040976 History: Received March 30, 2018; Revised July 19, 2018

In this paper, we use continuum mechanics to develop an analytic treatment of elastic wave scattering from an embedded cylinder and show that a classic treatise on the subject contains important errors for oblique angles of incidence, which we correct. We also develop missing equations for the scattering cross section at oblique angles and study the sensitivity of the scattering cross section as a function of elastodynamic contrast mechanisms. We find that in the Mie scattering regime for oblique angles of incidence, both elastic and density contrast are important mechanisms by which scattering can be controlled, but that their effects can offset one another, similar to the theory of reflection at flat interfaces. In comparison, we find that in the Rayleigh scattering regime, elastic and density contrast are always complimentary toward increasing scattering cross section, but for sufficiently high density contrast, the scattering cross section for incident compressional and y-transverse modes is nearly independent of elastic contrast. The solution developed captures the scattering physics for all possible incident elastic wave orientations, polarizations, and wavelengths including the transition from Rayleigh to geometric scattering regimes, so long as the continuum approximation holds. The method could, for example, enable calculation of the thermal conductivity tensor from microscopic principles which requires knowledge of the scattering cross section spanning all possible incident elastic wave orientations and polarizations at thermally excited wavelengths.

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References

White, R. M. , 1958, “ Elastic Wave Scattering at a Cylindrical Discontinuity in a Solid,” J. Acoust. Soc. Am., 30(8), pp. 771–785. [CrossRef]
Abramowitz, M. , and Stegun, I. A. , 1964, Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables, 9th ed, Dover, New York.
Kakodkar, R. R. , and Feser, J. P. , 2015, “ A Framework for Solving Atomistic Phonon-Structure Scattering Problems in the Frequency Domain Using Perfectly Matched Layer Boundaries,” J. Appl. Phys., 118(9), p. 094301. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Coordinate axes and angle definitions for the scattering problem. Vector â lies in plane xz.

Grahic Jump Location
Fig. 2

Scattering efficiency of NiSi2 cylinders in Si0.5Ge0.5 as a function of scattering parameter at normal angle-of-incidence for different incident polarizations. Black lines indicate the total scattering efficiency, while symbols indicate the portion scattered into compressional (box), y-transverse (circle), and quasi-z-transverse modes (cross).

Grahic Jump Location
Fig. 3

Scattering efficiency of NiSi2 cylinders in Si0.5Ge0.5 as a function of scattering parameter at normal angle-of-incidence for different incident polarizations. Black lines indicate the total scattering efficiency, while symbols indicate the portion scattered into compressional (box), y-transverse (circle), and quasi-z-transverse modes (cross).

Grahic Jump Location
Fig. 4

Scattering efficiency as a function of relative elastic and density contrast in the Mie regime (ka = 2) at an oblique angle of incidence, ϕ2 = 35 deg (longitudinal) or ψ2 = 35 deg (transverse)

Grahic Jump Location
Fig. 5

αQ/(2k3a4) as a function of relative elastic and density contrast in the Rayleigh regime (ka ≪ 1) at an oblique angle of incidence, ϕ2 = 35 deg (longitudinal) or ψ2 = 35 deg (transverse)

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