Selvam Sundaraelangovan, Volker Arno, van Neer Paul, de Jong Nico, Verweij Martin D
Laboratory of Medical Imaging, Department of Imaging Physics, Delft University of Technology, Delft, Netherlands.
Acoustics and Sonar, TNO, The Hague, Netherlands.
J Acoust Soc Am. 2022 May;151(5):3316. doi: 10.1121/10.0010448.
Over the last 15 years, literature on nondestructive testing has shown that the generation of higher harmonics and nonlinear mixing of waves could be used to obtain the nonlinearity parameters of an elastic medium and thereby gather information about its state, e.g., aging and fatigue. To design ultrasound measurement setups based on these phenomena, efficient numerical modeling tools are needed. In this paper, the iterative nonlinear contrast source method for numerical modeling of nonlinear acoustic waves is extended to the one-dimensional elastic case. In particular, nonlinear mixing of two collinear bulk waves (one compressional, one shear) in a homogeneous, isotropic medium is considered, taking into account its third-order elastic constants ( A, B, and C). The obtained results for nonlinear propagation are in good agreement with a benchmark solution based on the modified Burgers equation. The results for the resonant waves that are caused by the one-way and two-way mixing of primary waves are in quantitative agreement with the results in the literature [Chen, Tang, Zhao, Jacobs, and Qu, J. Acoust. Soc. Am. 136(5), 2389-2404 (2014)]. The contrast source approach allows the identification of the propagating and evanescent components of the scattered wavefield in the wavenumber-frequency domain, which provides physical insight into the mixing process and explains the propagation direction of the resonant wave.
在过去的15年里，无损检测领域的文献表明，利用高次谐波的产生和波的非线性混合可以获取弹性介质的非线性参数，从而收集有关其状态的信息，例如老化和疲劳情况。为了基于这些现象设计超声测量装置，需要高效的数值建模工具。在本文中，用于非线性声波数值建模的迭代非线性对比源方法被扩展到一维弹性情况。特别地，考虑了在均匀各向同性介质中两个共线体波（一个纵波，一个横波）的非线性混合，并考虑了其三阶弹性常数（A、B和C）。得到的非线性传播结果与基于修正伯格斯方程的基准解吻合良好。由一次波的单向和双向混合引起的共振波结果与文献[Chen, Tang, Zhao, Jacobs, and Qu, J. Acoust. Soc. Am. 136(5), 2389-2404 (2014)]中的结果在定量上一致。对比源方法能够在波数 - 频率域中识别散射波场的传播分量和消逝分量，这为混合过程提供了物理见解，并解释了共振波的传播方向。
