Karima Khusnutdinova

Layered (or laminated) structures are increasingly used in modern constructions and devices. Integrity of such structures is mainly determined by the quality of their interfaces: poor adhesion or delamination can lead to a catastrophic failure of the whole structure. Can nonlinear waves help us to detect such defects? In this talk I will discuss our recent analytical and experimental studies of long nonlinear waves in layered elastic waveguides, including wave scattering by inhomogeneities modelling poor adhesion or delamination. The emphasis is on classical and radiating solitary waves. In particular, we study the dynamics of a long longitudinal strain solitary wave in a split, symmetric layered bar, made of nonlinearly elastic (Murnaghan) material. The developed approach is based on matching two asymptotic multiple-scale expansions, integrability theory of the leading order KdV equations by the Inverse Scattering Transform and some natural radiation conditions. We show that splitting of the layered structure induces the generation of a train of secondary solitary waves from a single incident soliton and, thus, can be used to detect the defect. The theory is supported by experiments, performed in the Ioffe Institute in St. Petersburg (Russia), using holographic interferometry and laser induced generation of a compression solitary wave in two- and three-layered polymethylmethacrylate (PMMA) bars, bonded using ethyl cyanoacrylate- based (CA) adhesive.