Abstract Summary
The non-linear dynamics of layered structures are highly dependent on the material and bonding between each layer; a lack of proper alignment, or delamination, could lead to deleterious outcomes including structural failure. Experiments on different types of thin-walled cylindrical shells have recently been carried out, showing that delamination can be detected by changes in the transmitted wave field [1]. The long longitudinal strain waves in a two-layered waveguide can be modelled by coupled Boussinesq equation [2]. In this talk, we will focus on the reduced case, when the lower layer of the waveguide to be significantly denser than the upper layer, leading to a system of Boussinesq-Klein-Gordon (BKG) equations [3]. We consider a two layered waveguide with a de-lamination in the centre and soft (imperfect) bonding either side of the centre. Direct numerical modelling is difficult and so I will use a semi-analytical approach using asymptotic methods, which leads to Ostrovsky equations in soft bonded regions and Korteweg-de Vries equations in the delaminated region. The semi-analytical approach and direct numerical simulations are in good agreement. We will also discuss how the dispersion relation is used to determine the wave speed and hence classify the length of the delamination, in addition to changes in the amplitude of the wave packet. These results can provide a tool to control the integrity of layered structures. We will also discuss recent results for the case when the materials of the upper and lower layers are similar, and thus the structure is modelled by coupled Boussinesq equations. Using a similar approach, the delamination length can be inferred from changes in the transmitted wave field. References [1] G.V. Dreiden, A.M. Samsonov, I.V. Semenova, A.G. Shvartz, Strain solitary waves in a thinwalled waveguide. Appl. Phys. Lett. 105, 211906 (2014). [2] K.R. Khusnutdinova, A.M. Samsonov, A.S. Zakharov, Nonlinear layered lattice model and generalized solitary waves in imperfectly bonded structures. Phys. Rev. E 79, 056606 (2009). [3] J.S. Tamber and M.R. Tranter, Scattering of an Ostrovsky wave packet in a delaminated waveguide. Wave Motion, 114, 103023 (2022).
