Scattering waves in elastic waveguides

4 June 2009
Karima Khusnutdinova
Layered (or laminated) structures are increasingly used in modern industry (e.g., in microelectronics and aerospace engineering). 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? We study the dynamics of a nonlinear longitudinal bulk strain wave in a split, layered elastic bar, made of nonlinearly hyperelastic Murnaghan material. We consider a symmetric two-layered bar and assume that there is perfect interface for x < 0 and splitting for x > 0, where the x-axis is directed along the bar. Using matched asymptotic multiple-scales expansions and the integrability theory of the KdV equation by the Inverse Scattering Transform, we examine scattering of solitary waves and show that the defect causes generation of more than one secondary solitary waves from a single incident soliton and, thus, can be used to detect the defect. The theory is supported by experimental results. Experiments have been performed in the Ioffe Institute in St. Petersburg (Russia), using holographic interferometry and laser induced generation of an incident compression solitary wave in two- and three-layered polymethylmethacrylate (PMMA) bars, bonded using ethyl cyanoacrylate-based (CA) adhesive.
  • Differential Equations and Applications Seminar