Nonlinear clapping modulation of lamb modes by normally closed delamination

The nonlinear interaction between a high-frequency probing Lamb mode, propagating through a bilayer containing an initially closed tangential delamination at the interlayer interface whose contact conditions are dynamically changing because of a high-amplitude Lamb pump wave with long wavelength, is modeled in a quasi-stationary approach. The proposed criterion for the delamination to open is based on the magnitude, with respect to a threshold value, of the pump-wave-induced normal stress components that are pulling on both sides of the interface during part of its cycle. The temporal evolution of the contact condition during the pump wave cycle is calculated and the spectral enrichment caused by cross-modulation spectral components between the probing wave and the modulating wave is predicted. The impact of the cross-modulation on the normal displacement at the externally accessible surfaces is investigated for two different types of incident probing wave in an absorbing bilayer structure, and for different variations of the contact quality modulation. The results can serve as a parametric guide for experimenters considering the use of nonlinear harmonic generation of Lamb waves as a tool for nondestructive testing of bilayers such as rubber-steel composite walls that are typically used in storage tanks and pipelines for corrosive liquids.