Shear-lag solution for excitation, sensing, and time reversal of Lamb waves for structural health monitoring

Abstract

An analytical solution is presented for excitation, forward propagation, sensing, and time reversal of Lamb waves, considering the shear-lag effect of the bonding layer between the piezoelectric patch transducers and the plate. Consistent shear-lag solutions for actuator–plate and plate–sensor interactions are developed, considering plane strain condition. The Lamb wave solution is obtained by transforming the interfacial shear stress distribution and wave equations into the wavenumber domain by applying the spatial Fourier transform and converting the same to the physical domain using the inverse Fourier transform and residue theorem. The time-domain response for an arbitrary excitation is obtained by applying the temporal Fourier transform to the excitation and using convolution integral. The solution is compared with the experimental and numerical results for both forward and time-reversal responses and also for the best reconstruction frequency. The effect of transducer mass on the accuracy of the response is investigated. Finally, the shear-lag effect on the time reversibility of the reconstructed signal is studied for varying adhesive layer thickness, transducer thickness, host plate thickness, and the tone burst count. The solution will be useful for designing structural health monitoring systems using both baseline-based and baseline-free methods.