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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February 2019
Research-Article
A Mode-Resolved Continuum Mechanics Model of Acoustic Wave Scattering From Embedded Cylinders
Vineet Unni,
Vineet Unni
Department of Mechanical Engineering,
University of Delaware,
Newark, DE 19716
e-mail: vineetu@udel.edu
University of Delaware,
Newark, DE 19716
e-mail: vineetu@udel.edu
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Joseph P. Feser
Joseph P. Feser
Department of Mechanical Engineering,
University of Delaware,
Newark, DE 19716
e-mail: jpfeser@udel.edu
University of Delaware,
Newark, DE 19716
e-mail: jpfeser@udel.edu
Search for other works by this author on:
Vineet Unni
Department of Mechanical Engineering,
University of Delaware,
Newark, DE 19716
e-mail: vineetu@udel.edu
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
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. Feb 2019, 141(1): 011015 (9 pages)
Published Online: September 10, 2018
Article history
Received:
March 30, 2018
Revised:
July 19, 2018
Citation
Unni, V., and Feser, J. P. (September 10, 2018). "A Mode-Resolved Continuum Mechanics Model of Acoustic Wave Scattering From Embedded Cylinders." ASME. J. Vib. Acoust. February 2019; 141(1): 011015. https://doi.org/10.1115/1.4040976
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