Validation of zero-group-velocity feature guided waves in a welded joint.

Extensive research has been conducted on zero-group-velocity (ZGV) Lamb waves in elastic plates, demonstrating significant progress in the field of nondestructive testing. However, there is a scarcity of studies focusing on ZGV modes in complex structures. In this paper, we present our research investigating the presence of ZGV feature guided waves (FGWs) in a welded joint. Our approach follows a similar methodology used to study ZGV Lamb waves in elastic plates. By employing two-dimensional (2D) finite element (FE) modeling, we analyze the response spectra of the welded joint when subjected to a force source, revealing the occurrence of resonance in the response spectra. To investigate resonance modes in the welded joint, we employ the three-dimensional (3D) time-step FE method. By applying spatial 2D and short-time Fourier transforms to the received time-domain signals, we analyze the frequency content and spatial distribution of the signals. This analysis allows us to verify the existence of non-propagation and propagation modes in the welded joint. The non-propagation mode refers to the presence of signals with a zero wavenumber, indicating that they do not propagate or travel along the welded joint. These signals are typically associated with local resonances or vibrations within the welded joint itself. On the other hand, the propagation mode corresponds to signals with nonzero wavenumbers, suggesting that they propagate or travel along the welded joint. Furthermore, by further analyzing the propagation mode in the welded joint, similar to the analysis of ZGV modes in solid plates, we have observed that it also exhibits ZGV characteristics based on the wavenumber-frequency spectra. To further analyze acoustic field distributions at resonance frequencies, we utilize the semi-analytical finite element method in conjunction with the perfectly matched layer method. The results obtained from this analysis are consistent with those obtained from the 2D FE method and 3D time-step FE method, thereby confirming that propagation modes with ZGV characteristics at resonance frequencies correspond to FGWs, which we refer to as ZGV-FGWs. Through this step-by-step analysis, we ultimately establish the existence of ZGV-FGWs in the welded joint. This study introduces fresh ideas and serves as a point of reference for future research on ZGV-FGWs in complex structures.