@inproceedings{46de68ac87f246ee871820b49d1a567e,
title = "Wave propagation in elastic medium with heterogeneous quadratic nonlinearity",
abstract = "This paper studies the one-dimensional wave propagation in an elastic medium with spatially non-uniform quadratic nonlinearity. Two problems are solved analytically. One is for a time-harmonic wave propagating in a half-space where the displacement is prescribed on the surface of the half-space. It is found that spatial non-uniformity of the material nonlinearity causes backscattering of the second order harmonic, which when combined with the forward propagating waves generates a standing wave in steady-state wave motion. The second problem solved is the reflection from and transmission through a layer of finite thickness embedded in an otherwise linearly elastic medium of infinite extent, where it is assumed that the layer has a spatially non-uniform quadratic nonlinearity. The results show that the transmission coefficient for the second order harmonic is proportional to the spatial average of the nonlinearity across the thickness of the layer, independent of the spatial distribution of the nonlinearity. On the other hand, the coefficient of reflection is proportional to a weighted average of the nonlinearity across the layer thickness. The weight function in this weighted average is related to the propagating phase, thus making the coefficient of reflection dependent on the spatial distribution of the nonlinearity. Finally, the paper concludes with some discussions on how to use the reflected and transmitted second harmonic waves to evaluate the variance and autocorrelation length of nonlinear parameter β when the nonlinearity distribution in the layer is a stochastic process.",
keywords = "Elastic Media, Finite Amplitude, Heterogeneous Nonlinearity, Longitudinal Wave, Nonlinear theory",
author = "Guangxin Tang and Jacobs, {Laurence J.} and Jianmin Qu",
year = "2011",
doi = "10.1063/1.3591838",
language = "English",
isbn = "9780735408883",
series = "AIP Conference Proceedings",
pages = "43--50",
booktitle = "Review of Progress in Quantitative Nondestructive Evaluation",
note = "37th Annual Review of Progress in Quantitative Nondestructive Evaluation, QNDE ; Conference date: 18-07-2010 Through 23-07-2010",
}