Abstract The propagation characteristics of feature guided waves (FGWs) in topographical waveguides, such as welded joints, have been widely investigated. However, most of these investigations analyzed linear acoustic characteristics. Considering the high sensitivity of nonlinear ultrasonic techniques in the nondestructive evaluation of microscopic defects in materials, such as identifying micro-defects at an early stage, it is particularly relevant to investigate the nonlinear acoustic response of FGWs in topographical waveguides. In this paper, we use a theoretical analysis and numerical simulation to investigate the second-harmonic generation (SHG) of FGWs in a welded joint. The theoretical framework is firstly expounded based on the reciprocity relation and modal expansion with the nonlinear semi-analytical finite element (SAFE) method and perfectly matched layers. Numerical models are implemented to predict the effect of SHG of FGWs in a welded joint. Two families of FGW propagation in a welded joint are analyzed. The results obtained demonstrate that mode conversion and the cumulative effect of the generated second harmonics can be observed in the welded joint. This investigation provides new physical insights into SHG for FGW propagation.

中文翻译：

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焊接接头中特征导波非线性声学响应的理论和数值研究

摘要 特征导波 (FGW) 在焊缝等地形波导中的传播特性已得到广泛研究。然而，大多数这些调查分析了线性声学特性。考虑到非线性超声技术在材料微观缺陷无损评估中的高灵敏度，例如早期识别微观缺陷，研究拓扑波导中 FGW 的非线性声学响应尤为重要。在本文中，我们使用理论分析和数值模拟来研究焊接接头中 FGW 的二次谐波产生 (SHG)。首先利用非线性半解析有限元(SAFE)方法和完美匹配层，基于互易关系和模态展开，阐述了理论框架。实施数值模型来预测焊接接头中 FGW 的 SHG 效果。分析了焊接接头中 FGW 传播的两个家族。获得的结果表明，在焊接接头中可以观察到模式转换和产生的二次谐波的累积效应。这项研究为 FGW 传播的 SHG 提供了新的物理见解。获得的结果表明，在焊接接头中可以观察到模式转换和产生的二次谐波的累积效应。这项研究为 FGW 传播的 SHG 提供了新的物理见解。获得的结果表明，在焊接接头中可以观察到模式转换和产生的二次谐波的累积效应。这项研究为 FGW 传播的 SHG 提供了新的物理见解。