论文标题
弹性板中的小形状缺陷反转的羔羊模式和天生的近似
Lamb modes and Born approximation for small shape defects inversion in elastic plates
论文作者
论文摘要
这项工作的目的是提出理论工具，以研究弹性波导中的波传播并执行多频散射反转以在2D和3D弹性板中重建小形状缺陷。给定表面多频波场测量值，我们使用天生的近似值来重建板的几何形状中的局部缺陷。为了证明这种近似值，我们引入了一个严格的框架，以研究由任意来源产生的弹性波场的传播。通过研究一系列不均匀羔羊模式的降低速率，我们证明了PDE的适当性，该PDE模拟了2D和3D平面波导中的弹性波传播。我们还表征了羔羊分解无效的关键频率。使用这些结果，我们将已经为声学波导开发的形状重建方法推广到2D弹性波导，并基于散射场给出的模式的逐种模式的空间傅立叶反转提供了稳定的重建方法。
The aim of this work is to present theoretical tools to study wave propagation in elastic waveguides and perform multi-frequency scattering inversion to reconstruct small shape defects in a 2D and 3D elastic plate. Given surface multi-frequency wavefield measurements, we use a Born approximation to reconstruct localized defect in the geometry of the plate. To justify this approximation, we introduce a rigorous framework to study the propagation of elastic wavefield generated by arbitrary sources. By studying the decreasing rate of the series of inhomogeneous Lamb mode, we prove the well-posedness of the PDE that model elastic wave propagation in 2D and 3D planar waveguides. We also characterize the critical frequencies for which the Lamb decomposition is not valid. Using these results, we generalize the shape reconstruction method already developed for acoustic waveguide to 2D elastic waveguides and provide a stable reconstruction method based on a mode-by-mode spacial Fourier inversion given by the scattered field.
