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.

翻译：在无损评估导波检测中，待检测的弹性结构常嵌入其他弹性介质内，由此产生的泄漏波计算复杂且非平凡；我们考虑弹性波导被其他弹性材料包围的典型示例，该示例揭示了在此类系统中计算泄漏波的基本问题。由于表示泄漏波需要复波数解，现有数值方法面临重大挑战——通过对场进行空间离散化来获取泄漏波的方法，会因波幅在深入周围介质时呈指数增长而失效。本文提出一种谱配置方法，能够准确高效地识别这些向弹性半空间泄漏的模态。我们对弹性域进行离散化，并根据外部体波速度，将离散域映射到适当的复路径，使数值解在该路径上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形，我们成功获取了完整的频散和衰减曲线，并在可能情况下使用商用软件DISPERSE进行了验证。作为独立验证，通过傅里叶分析对瞬态波进行有限元模拟，同样获得了频散曲线。