Viscoelastically coupled multi-layered spectral elements for analyzing ultrasonic-guided wave propagation in layered structural waveguides: part 1—CLT and GMM

This paper presents viscoelastically coupled multi-layered spectral elements for analyzing ultrasonic-guided wave propagation in layered structural waveguides through different modeling approaches by approximating them as higher-order frames (Mindlin–Herrmann rod + Timoshenko beam). The approaches are categorized into two types based on the modeling of the interface bonding layer. The first type assumes perfect bonding between the layers. However, real structures often exhibit imperfect or weak bonding, resulting in reduced interface bonding strength. To account for this, the second type employs the combination of distributed spring-dashpot systems to model the interface bonding layer, capturing its viscoelastic nature. This allows for the simulation of different bonding layer strengths by adjusting the spring and damping constants. We have introduced the concept of effective thickness to match the cut-off frequencies in the dispersion curves obtained from the developed approaches with those of exact Lamb waves, which are used in determining the shear correction factors necessary for higher-order frame formulations. The time-domain responses obtained from developed Spectral Elements are validated against Finite Element simulations conducted in COMSOL and experimental results. In the last part of this paper, we have explored the interaction of ultrasonic-guided waves with defects such as delamination or debonding.