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2 Engineering Transactions

2 2024

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Wavelet analysis of ultrasonic lamb wave displacements in three-layer adhesive plates: continuous wavelet transform (CWT) versus the semi-analytical finite element method (SAFEM)

Yacoubi Abdelali, Jabiri Ayoub, Azkour Mustapha, Mandry Rachid, Allami Mhammed El

Engineering Transactions

2024

Vol. 72, iss. 2

203--224

In this paper, we aim to identify the most appropriate mother wavelet for analyzing the displacements of ultrasonic guided waves in tri-layered adhesive plates.We determine the group velocities of a given mode using various mother wavelets. The precision of each mother wavelet is evaluated by comparing the values of the group velocities with those found by the semianalytical finite element method (SAFEM). The most appropriate mother wavelet function can then be used to study tri-layered adhesive plates with defects.

Calculation of the dispersion curves modeling the propagation of ultrasonic Lamb waves in a bonded aluminum/epoxy/aluminum structure using the semi-analytical finite element method

Azkour Mustapha, Allami Mhammed El, Rhimini Hassan

Engineering Transactions

2024

Vol. 72, iss. 2

119--143

The main aim of this paper is to calculate the dispersion curves modeling the propagation of ultrasonic Lamb waves inside a bonded tri-layer plane aluminum/epoxy/aluminum structure using the semi-analytical finite element (SAFE) method. The paper also aims to plot the nodal displacements normalized by their maximums for the four propagative modes that appear at the frequency of 200 kHz. These results contribute to the understanding of ultrasonic wave propagation in planar multilayer structures and have potential applications in non-destructive testing. The SAFE method is compared to the Graphical User Interface for Guided Ultrasonic Waves GUIGUW program. In general, this paper highlights the particular dispersive behavior of ultrasonic guided waves propagating in bonded three-layer structures. The GUIGUW program has been rarely utilized by authors to verify and compare results, particularly for this kind of structure, despite its robustness in calculating ultrasonic guided waves’ dispersion curves. We are still among the few who have drawn this parallel. In this paper, we put forth a very clear-cut and accurate framework for determining the dispersion curves of a three-layer structure, and researchers who are new to the SAFE method may find this framework helpful as well. Another result shown in this paper is that the S0 mode is more sensitive to changes in the epoxy layer thickness than the A0 mode in the low-frequency range. Therefore, we can determine how much resin epoxy adhesive layer is missing from two ostensibly identical structures by estimating the difference in adhesive thickness. One of the structures is used as a reference, and the variation in phase velocity can allow the estimation of the lack of resin epoxy. However, if we want to assess defects such as debonding using the S0 mode, a low frequency should be used, and it must be strictly smaller than its frequency of high dispersivity and correspond to a maximum group velocity.