非线性固体中剪切声束的双曲框架
A hyperbolic framework for shear sound beams in nonlinear solids
摘要：
在软弹性固体中，当同时考虑二次非线性和三次非线性时，方向剪切波一般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。我们提出了一个变量的变化，将方程转化为一个准线性一阶偏微分方程组。其数值解决方案，然后使用路径保守的MUSCL-Osher有限体积格式，这是非常适合于计算的冲击波。我们验证的方法对解析解（格林函数，平面波）。结果突出的奇次谐波和二阶谐波的高斯剪切波光束的产生。
英文摘要：
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.
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