各向同性无限板中对称空腔缺陷对 Lamb 波与 SH 导波散射的三维 DtN-FEM 分析
Three-dimensional DtN-FEM scattering analysis of Lamb and SH guided waves by a symmetric cavity defect in an isotropic infinite plate
AI总结：
提出三维 DtN-FEM，利用导波叠加与模态正交性建立虚拟边界 DtN 条件，分析无限板中对称空腔缺陷对 Lamb 和 SH 波的散射，并可直接获得各模态反射、透射系数。
摘要：
本文发展了一种三维 Dirichlet-to-Neumann（DtN）有限元方法（FEM），用于分析各向同性无限板中对称空腔缺陷引起的 Lamb 波和 SH 导波散射。在有限元分析过程中，需要在位移和面力均未知的虚拟边界上确定远场 DtN 条件。本研究首先将虚拟边界处的散射波表示为具有未知散射系数的导波叠加。其次，利用模态正交性，通过散射系数，将虚拟边界处的未知面力表示为虚拟边界处未知散射位移的形式。第三，虚拟边界处的这一关系最终可组装进全局 DtN-FEM 矩阵以求解该问题。该方法简洁精巧，具有降维优势；与传统 FEM 相比，无需吸收介质或完全匹配层来抑制反射波。此外，无需后处理即可直接获得各导波模态的反射系数和透射系数。所提出的三维 DtN-FEM 将与边界元法（BEM）进行比较，并最终通过若干基准问题得到验证。
英文摘要：
In this paper, a three-dimensional Dirichlet-to-Neumann (DtN) finite element method (FEM) is developed to analyze the scattering of Lamb and SH guided waves due to a symmetric cavity defect in an isotropic infinite plate. During the finite element analysis, it is necessary to determine the far-field DtN conditions at virtual boundaries where both displacements and tractions are unknown. In this study, firstly, the scattered waves at the virtual boundaries are represented by a superposition of guided waves with unknown scattered coefficients. Secondly, utilizing the mode orthogonality, the unknown tractions at virtual boundaries are expressed in terms of the unknown scattered displacements at virtual boundaries via scattered coefficients. Thirdly, this relationship at virtual boundaries can be finally assembled into the global DtN-FEM matrix to solve the problem. This method is simple and elegant, which has advantages on dimension reduction and needs no absorption medium or perfectly matched layer to suppress the reflected waves compared to traditional FEM. Furthermore, the reflection and transmission coefficients of each guided mode can be directly obtained without post-processing. This proposed 3D DtN-FEM will be compared with boundary element method (BEM) and finally validated for several benchmark problems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
