Three-dimensional DtN-FEM scattering analysis of Lamb and SH guided waves by a symmetric cavity defect in an isotropic infinite plate

TL;DR

This paper introduces a 3D DtN-FEM approach for analyzing Lamb and SH wave scattering by a symmetric cavity in an infinite plate, offering advantages in dimension reduction and direct mode coefficient extraction.

Contribution

The paper develops a novel 3D DtN-FEM method that simplifies scattering analysis without needing absorption layers, enabling direct calculation of mode reflection and transmission coefficients.

Findings

Accurately predicts scattering and mode coefficients.

Demonstrates advantages over traditional FEM and BEM.

Validated against benchmark problems.

Abstract

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.