Wave scattering by an elastic inclusion with quadratic nonlinearity

Guangxin Tang, Laurence J. Jacobs, Jianmin Qu

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

Abstract

This paper studies the problem of three-dimensional wave scattering by an elastic inclusion with quadratic nonlinearity in an otherwise linear elastic medium. Due to the nonlinearity of the inclusion, second order wave appears in the scattered field. Under the incidence of a plane longitudinal wave, solution to the scattered second order field is derived explicitly in terms of the Green's function. A far field approximation of the scattered field is also obtained. The results of far field show that the scattered second harmonic field consists of a longitudinal spherical wave and a shear spherical wave. Furthermore, it is found that the amplitude of the forward scattered field is proportional to the acoustic nonlinearity parameter β averaged over the volume of the inclusion, and the amplitude of backscattered field is proportional to a spatially weighted average of β. Finally, a method is described to nondestructively obtain the statistics of the spatial variation of β over the inclusion such as the mean, the variance and autocorrelation length.

Original languageEnglish
Title of host publicationReview of Progress in Quantitative Nondestructive Evaluation
Pages269-276
Number of pages8
Edition31
DOIs
StatePublished - 2012
Event38th Annual Review of Progress in Quantitative Nondestructive Evaluation, QNDE - Burlington, VT, United States
Duration: 17 Jul 201122 Jul 2011

Publication series

NameAIP Conference Proceedings
Number31
Volume1430
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

Conference38th Annual Review of Progress in Quantitative Nondestructive Evaluation, QNDE
Country/TerritoryUnited States
CityBurlington, VT
Period17/07/1122/07/11

Keywords

  • Heterogeneous
  • Longitudinal Wave
  • Quadratic Nonlinearity

Fingerprint

Dive into the research topics of 'Wave scattering by an elastic inclusion with quadratic nonlinearity'. Together they form a unique fingerprint.

Cite this