On the harmonic scattering amplitudes from a nonlinear elastic spherical inclusion

Christopher Kube, Andrea Arguelles, Brandon McWilliams

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper, the interaction of an incident finite amplitude longitudinal wave with a localized region of nonlinearity is considered. This interaction produces a secondary field represented by a superposition of first-, second-, and third-harmonic components. The secondary field is solely a result of the quadratic and cubic elastic nonlinearity present within the region of the inclusion. The second-harmonic scattering amplitude depends on the quadratic nonlinearity parameter β, while the first- and third-harmonic amplitudes depend on the cubic nonlinearity parameter γ. The special cases of forward and backward scattering amplitudes were analyzed. For each harmonic, the forward-scattering amplitude is always greater than or equal to the backward scattering amplitude in which the equality is only realized in the Rayleigh scattering limit. Lastly, the amplitudes of the scattered harmonic waves are compared to predicted harmonic amplitudes derived from a plane wave model.

Original languageEnglish (US)
Title of host publication44th Annual Review of Progress in Quantitative Nondestructive Evaluation, Volume 37
EditorsDale E. Chimenti, Leonard J. Bond
PublisherAmerican Institute of Physics Inc.
ISBN (Electronic)9780735416444
DOIs
StatePublished - Apr 20 2018
Event44th Annual Review of Progress in Quantitative Nondestructive Evaluation, QNDE 2017 - Provo, United States
Duration: Jul 16 2017Jul 21 2017

Publication series

NameAIP Conference Proceedings
Volume1949
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Other

Other44th Annual Review of Progress in Quantitative Nondestructive Evaluation, QNDE 2017
CountryUnited States
CityProvo
Period7/16/177/21/17

Fingerprint

scattering amplitude
inclusions
harmonics
nonlinearity
forward scattering
longitudinal waves
Rayleigh scattering
plane waves
interactions

All Science Journal Classification (ASJC) codes

  • Ecology, Evolution, Behavior and Systematics
  • Ecology
  • Plant Science
  • Physics and Astronomy(all)
  • Nature and Landscape Conservation

Cite this

Kube, C., Arguelles, A., & McWilliams, B. (2018). On the harmonic scattering amplitudes from a nonlinear elastic spherical inclusion. In D. E. Chimenti, & L. J. Bond (Eds.), 44th Annual Review of Progress in Quantitative Nondestructive Evaluation, Volume 37 [070004] (AIP Conference Proceedings; Vol. 1949). American Institute of Physics Inc.. https://doi.org/10.1063/1.5031556
Kube, Christopher ; Arguelles, Andrea ; McWilliams, Brandon. / On the harmonic scattering amplitudes from a nonlinear elastic spherical inclusion. 44th Annual Review of Progress in Quantitative Nondestructive Evaluation, Volume 37. editor / Dale E. Chimenti ; Leonard J. Bond. American Institute of Physics Inc., 2018. (AIP Conference Proceedings).
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Kube, C, Arguelles, A & McWilliams, B 2018, On the harmonic scattering amplitudes from a nonlinear elastic spherical inclusion. in DE Chimenti & LJ Bond (eds), 44th Annual Review of Progress in Quantitative Nondestructive Evaluation, Volume 37., 070004, AIP Conference Proceedings, vol. 1949, American Institute of Physics Inc., 44th Annual Review of Progress in Quantitative Nondestructive Evaluation, QNDE 2017, Provo, United States, 7/16/17. https://doi.org/10.1063/1.5031556

On the harmonic scattering amplitudes from a nonlinear elastic spherical inclusion. / Kube, Christopher; Arguelles, Andrea; McWilliams, Brandon.

44th Annual Review of Progress in Quantitative Nondestructive Evaluation, Volume 37. ed. / Dale E. Chimenti; Leonard J. Bond. American Institute of Physics Inc., 2018. 070004 (AIP Conference Proceedings; Vol. 1949).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Kube C, Arguelles A, McWilliams B. On the harmonic scattering amplitudes from a nonlinear elastic spherical inclusion. In Chimenti DE, Bond LJ, editors, 44th Annual Review of Progress in Quantitative Nondestructive Evaluation, Volume 37. American Institute of Physics Inc. 2018. 070004. (AIP Conference Proceedings). https://doi.org/10.1063/1.5031556