Wave propagation in adhesively bonded metallic and composite lap joints modelled through spectrally formulated elastically coupled double beam element

In this paper we describe a computational model based on frequency domain spectral finite element method (SFEM) developed to study wave propagation in metallic as well as composite adhesively bonded single lap joints. The single lap joint is modelled using spectrally formulated beam element and a new spectrally formulated elastically coupled double beam (ECDB) element. The ECDB element is used to represent the bonded region and is formulated as two axial-flexural-shear coupled beams coupled with continuously distributed elastic springs. The elastic springs model the adhesive bonding between two adherends. To understand the wave propagation in an adhesively bonded joint, first the dynamics of ECDB is studied in detail. With the help of dispersion curves, it is shown that there are six forward moving and six backward moving modes which exhibit complex coupled behaviour. As a result of this coupling, an additional cut-off frequency, which is a function of coupling spring stiffness, manifests in one of the bending modes propagating in an ECDB. First order shear deformable beams are used to model adherend top and bottom beams which introduce shear cut-off frequencies. The multiple cut-off frequencies in the system introduce multiple mode changes. In order to consolidate the understanding of an ECDB, high frequency wave propagation responses in various spectral ECDBs are studied and validated using Abaqus. Subsequently, wave propagation in different metallic and composite bonded joints is examined for perfectly and weakly bonded cases and numerical comparisons between the SFEM model and Abaqus are made. Finally, the SFEM models for the cases of perfectly bonded aluminium and symmetric ply laminated composite are experimentally validated. It is shown that the spectral ECDB element developed in this work may be used to model different levels of adhesion in any symmetric or asymmetric bonded joint comprising of only metals or composites or a combination of the two. Additionally, the spectral ECDB element may also be used to study other bonded structures like space platforms. Overall, the meagre computational requirement and short computational time ensured by the exact nature of dynamic stiffness matrices of the two spectral elements used makes this semi-analytical model a good aid for understanding ultrasonic wave propagation in adhesively bonded single lap joints.

Automated summary

This paper presents a computational model based on the frequency domain spectral finite element method (SFEM) for studying wave propagation in metallic and composite adhesively bonded single lap joints. The model uses spectrally formulated beam and ECDB elements to represent the joint. Through detailed analysis of the ECDB dynamics and validation of high frequency wave propagation responses, the model's accuracy and efficiency in understanding ultrasonic wave propagation in adhesively bonded joints are demonstrated.