Spectral analysis of the defective structural waveguides using the semi-analytical finite element method

Abstract

The spectral analysis of the structural waveguide leads to the dispersion relation, which shows the behavior of the different wavemodes with frequency. It helps in ultrasonic-guided wave-based non-destructive inspection to choose an excitation frequency based on the choice of the excitation wavemode(s). The dispersion curves for a waveguide with simple defect-free geometry work well for their inspection. However, the presence of any defect, e.g., delamination or cracks, affects the behavior of the propagating waves used for diagnostics. Therefore, it is necessary to perform the spectral analysis of the structural waveguide with defects and study the sensitivity of dispersion curves to the defect size, location, and orientation. The dispersion curves can be obtained analytically or numerically, but these methods have inherent limitations. The analytical techniques are limited to simple geometry; however, using numerical methods, e.g., Finite Element Method for complex geometry, will require a substantial computational cost. Therefore, this paper presents the spectral analysis of the three-dimensional structural waveguide with defects using the Semi-Analytical Finite Element Method, which uses the advantages of both analytical and numerical methods. It uses the analytical solution in the direction of wave propagation and numerical solutions in the transverse directions. We have performed the spectral analysis of defect-free and defective waveguides containing defects such as cracks or delamination of varying sizes, locations, and orientations. The finite element discretization of the cross-section affects the number and accuracy of wavemodes obtained in the dispersion curves. The computed dispersion curves for defect-free waveguides are compared with those obtained from open-source dispersion computation software GUIGUW (Bocchini et al.) for the same geometry and found a good match between them. As the defects reduce the structure’s stiffness, we observed a significant reduction in the cutoff frequencies of the higher-order wave modes in the dispersion curves for defective waveguides compared to their defect-free counterparts.