标题： 使用谱配置法计算弹性半空间之间的波导中的泄漏兰姆波 显示英文标题

标题： Computing leaky Lamb waves for waveguides between elastic half-spaces using spectral collocation

摘要： 在无损检测中的导波检测中，被检测的弹性结构通常嵌入在其他弹性介质中，由此产生的泄漏波是复杂的，且难以计算；我们考虑了一个典型的例子，即一个被其他弹性材料包围的弹性波导，该例子展示了在这种系统中计算泄漏波的基本问题。 由于需要表示它们的复数波数解，泄漏波对现有的数值方法提出了重大挑战，那些通过空间离散化场来获取它们的方法在远离周围介质时会受到其振幅指数增长的影响。 我们提出了一种谱配置方法，能够准确而高效地识别这些渗入弹性半空间的模式。 我们对弹性区域进行离散化，并根据外部体波速度选择适当的离散化区域到复数路径的映射，在这些路径中，数值解会衰减，同时保持问题的物理特性。 通过遍历所有可能的辐射情况，成功地检索并验证了完整的色散和衰减曲线，必要时与商用软件DISPERSE进行对比。 作为独立验证，通过使用傅里叶分析的时间依赖波的有限元模拟得到了色散曲线。 显示英文摘要

摘要： In non-destructive evaluation guided wave inspections, the elastic structure to be inspected is often embedded within other elastic media and the ensuing leaky waves are complex and non-trivial to compute; we consider the canonical example of an elastic waveguide surrounded by other elastic materials that demonstrates the fundamental issues with calculating the leaky waves in such systems. Due to the complex wavenumber solutions required to represent them, leaky waves pose significant challenges to existing numerical methods, with methods that spatially discretise the field to retrieve them suffering from the exponential growth of their amplitude far into the surrounding media. We present a spectral collocation method yielding an accurate and efficient identification of these modes, leaking into elastic half-spaces. We discretise the elastic domains and, depending on the exterior bulk wavespeeds, select appropriate mappings of the discretised domain to complex paths, in which the numerical solution decays and the physics of the problem are preserved. By iterating through all possible radiation cases, the full set of dispersion and attenuation curves are successfully retrieved and validated, where possible, against the commercially available software DISPERSE. As an independent validation, dispersion curves are obtained from finite element simulations of time-dependent waves using Fourier analysis.