Investigation of Lamb waves attenuation in elastic–viscoelastic three-layer adhesive joints in low and high frequencies: Theoretical modeling

In this paper the attenuation of Lamb waves in three-layer joints, including two elastic plates bonded together by a viscoelastic adhesive layer, is investigated in high and low frequencies using global matrix method. Theoretical boundary value problem in three-layer adhesive joints with perfect bond and traction-free boundary conditions on their outer surfaces is solved to find a combination of frequencies and modes with lowest attenuation. Characteristic equation is derived by applying continuity and boundary conditions in three-layer joints using global matrix method. Attenuation and phase velocity dispersion curves in high and low frequencies are obtained with numerical solution of this equation by a computer code for a three-layer joint, including an aluminum repair patch bonded to the aircraft aluminum skin by a layer of viscoelastic epoxy adhesive. To validate the numerical solution results of characteristic equation, wave structure curves are plotted for a special mode in two different frequencies in the adhesive joint. Also, attenuated displacement amplitude curves in a round-trip of Lamb wave along the adhesive joint are plotted to investigate the reduction of the signal amplitude generated by a single transducer. The purpose of present paper is to find a combination of frequencies and modes with minimum attenuation in high and low frequencies. These frequencies and modes are recognizable by transducers in inspections with Lamb waves because of low attenuation level.