论文标题
在各向异性弹性波导中计算零组速度点：全球和局部收敛的方法
Computing zero-group-velocity points in anisotropic elastic waveguides: Globally and locally convergent methods
论文作者
论文摘要
弹性波导的分散曲线表现出群速度消失的点，而波数却保持有限。这些是所谓的零组速度（ZGV）点。由于这些点的弹性动力能量仍然限制在源头附近，因此它们对结构的无损测试和定量表征具有实际意义。这些应用程序依赖于ZGV点的正确预测。在此贡献中，我们首先根据其他模态溶液的外观对各向异性板中的ZGV共振进行建模。由此产生的管理方程式被解释为两个参数特征值问题。随后，我们提出了三种互补的数值程序，能够在传统的轴向功率通量消失的常规意义上计算任意非解散性弹性波导中的ZGV点。第一种方法是全球收敛性，并保证找到所有ZGV点，但只能用于小问题。第二个过程是非常快速的，通常是可应用的牛顿型迭代，是局部收敛的，需要初始猜测。第三种方法结合了两种方法，并产生适用于大问题的过程，不需要初始猜测，并且很可能会找到所有ZGV点。该算法在“ GEW ZGV计算”（doi：10.5281/Zenodo.7537442）中实现。
Dispersion curves of elastic waveguides exhibit points where the group velocity vanishes while the wavenumber remains finite. These are the so-called zero-group-velocity (ZGV) points. As the elastodynamic energy at these points remains confined close to the source, they are of practical interest for nondestructive testing and quantitative characterization of structures. These applications rely on the correct prediction of the ZGV points. In this contribution, we first model the ZGV resonances in anisotropic plates based on the appearance of an additional modal solution. The resulting governing equation is interpreted as a two-parameter eigenvalue problem. Subsequently, we present three complementary numerical procedures capable of computing ZGV points in arbitrary nondissipative elastic waveguides in the conventional sense that their axial power flux vanishes. The first method is globally convergent and guarantees to find all ZGV points but can only be used for small problems. The second procedure is a very fast, generally-applicable, Newton-type iteration that is locally convergent and requires initial guesses. The third method combines both kinds of approaches and yields a procedure that is applicable to large problems, does not require initial guesses and is likely to find all ZGV points. The algorithms are implemented in "GEW ZGV computation" (doi: 10.5281/zenodo.7537442).
