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A hyperbolic framework for shear sound beams in nonlinear solids
Communications in Nonlinear Science and Numerical Simulation ( IF 3.9 ) Pub Date : 2021-09-08 , DOI: 10.1016/j.cnsns.2021.106036
Harold Berjamin 1 , Michel Destrade 1
Affiliation  

In soft elastic solids, directional shear waves are in general governed by coupled nonlinear KZK-type equations for the two transverse velocity components, when both quadratic nonlinearity and cubic nonlinearity are taken into account. Here we consider spatially two-dimensional wave fields. We propose a change of variables to transform the equations into a quasi-linear first-order system of partial differential equations. Its numerical resolution is then tackled by using a path-conservative MUSCL-Osher finite volume scheme, which is well-suited to the computation of shock waves. We validate the method against analytical solutions (Green’s function, plane waves). The results highlight the generation of odd harmonics and of second-order harmonics in a Gaussian shear-wave beam.



中文翻译:

非线性固体中剪切声束的双曲线框架

在软弹性固体中,当同时考虑二次非线性和三次非线性时,方向性横波通常由两个横向速度分量的耦合非线性 KZK 型方程控制。这里我们考虑空间二维波场。我们建议改变变量以将方程转换为偏微分方程的拟线性一阶系统。然后通过使用路径保守的 MUSCL-Osher 有限体积方案来解决其数值分辨率,该方案非常适合冲击波的计算。我们针对解析解(格林函数、平面波)验证了该方法。结果突出了高斯横波束中奇次谐波和二阶谐波的产生。

更新日期:2021-09-15
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