Engineering Transactions, 72, 2, pp. 119–143, 2024

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

Mustapha AZKOUR
Hassan II University

Regional Center for Education and Training Professions (CRMEF)

Hassan II University

The main aim of this paper is to present calculating 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.

Keywords: non-destructive testing; bonded structures; ultrasonic guided waves; Lamb waves; semi-analytical finite element method; GUIGUW
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DOI: 10.24423/EngTrans.3171.2024