PSI - Issue 52

Feifei Ren et al. / Procedia Structural Integrity 52 (2024) 730–739 Author name / Structural Integrity Procedia 00 (2023) 000–000

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Fig. 1. The Theoretical results of dispersion curve, (a) wavenumber; (b) phase velocity; (c) group velocity.

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Fig. 2. The dispersion results with the change of temperature, (a) phase velocity; (b) group velocity.

results are shown in Figure 1. The dispersion curve of Lamb waves exhibits multiple modes, indicating the presence of distinct wave propagation characteristics associated with each mode. The dispersion curves provide information regarding the relationship of the group velocity with frequency and thicknesses and help with the determination of the cut-o ff frequency and non-dispersion area. To ensure the presence of only A 0 and S 0 modes and avoid higher order modes e ff ects, the determination of cut-o ff frequency is reported, which is 840 kHz · mm. This means that the product of frequency and thickness f · d should be selected below the cuto ff frequency, which for 2 mm panels is around 420 kHz. The stable group velocity range is also determined and it is used for further analysis of the tem perature e ff ect on the group velocity. Based on the mechanical test conducted to assess the temperature-dependent changes in material properties, the variations in group velocity with temperature are shown in Figure 2. It shows that the group velocity exhibits a constant change within a specific range of f · d . The responses of group velocity to temperature remain consistent within an approximate f · d range of [200 kHz · mm − 840 kHz · mm] for the A 0 and [0kHz · mm − 500 kHz · mm] for the S 0 mode.

4.2. Sensitivity Analysis of Group Velocity Change with Temperature

Temperature variations exert a significant impact on the propagation characteristics of guided waves, highlighting the need for a sensitivity analysis of group velocity to assess their influence. This analysis holds great importance in the development of reliable monitoring and inspection systems. By quantifying the sensitivity, the e ff ect of temper-