论文标题
在不均匀圆柱形壳中的弯曲弹性波的分支流动
Branched flows of flexural elastic waves in non-uniform cylindrical shells
论文作者
论文摘要
沿圆柱形壳的轴的弹性波的传播由于无处不在的存在和技术重要性，因此具有极大的当前感兴趣。在此类结构中，不可避免的是，几何缺陷和性质的空间变化是不可避免的。在这里，我们报告了这种波导中弯曲波的分支流的存在。高振幅运动的位置，远离发射位置，就差异而言，相对于弯曲刚度在空间变化的相关长度方面，缩放为功率定律。这些缩放定律从理论上源自射线方程。射线方程的数值集成也表现出与有限元数值模拟以及理论得出的缩放的这种行为一致性。对于过去的其他类型的波浪，缩放指数中的指数似乎是一种普遍性，以及弹性和弹性板中的分散波。
Propagation of elastic waves along the axis of cylindrical shells is of great current interest due to their ubiquitous presence and technological importance. Geometric imperfections and spatial variations of properties are inevitable in such structures. Here we report the existence of branched flows of flexural waves in such waveguides. The location of high amplitude motion, away from the launch location, scales as a power law with respect to the variance and linearly with respect to the correlation length of the spatial variation in the bending stiffness. These scaling laws are then theoretically derived from the ray equations. Numerical integration of the ray equations also exhibit this behaviour-consistent with finite element numerical simulations as well as the theoretically derived scaling. There appears to be a universality for the exponents in the scaling with respect to similar observations in the past for other types of waves, as well as flexural and hence dispersive waves in elastic plates.
