TY - GEN
T1 - Wave scattering by an elastic inclusion with quadratic nonlinearity
AU - Tang, Guangxin
AU - Jacobs, Laurence J.
AU - Qu, Jianmin
PY - 2012
Y1 - 2012
N2 - 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.
AB - 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.
KW - Heterogeneous
KW - Longitudinal Wave
KW - Quadratic Nonlinearity
UR - http://www.scopus.com/inward/record.url?scp=84863619445&partnerID=8YFLogxK
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U2 - 10.1063/1.4716239
DO - 10.1063/1.4716239
M3 - Conference contribution
AN - SCOPUS:84863619445
SN - 9780735410138
T3 - AIP Conference Proceedings
SP - 269
EP - 276
BT - Review of Progress in Quantitative Nondestructive Evaluation
T2 - 38th Annual Review of Progress in Quantitative Nondestructive Evaluation, QNDE
Y2 - 17 July 2011 through 22 July 2011
ER -