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.

Structural health monitoring of adhesive joints using Lamb waves: A review

“…Some data processing methods have been used within the LW‐based SHM approach for de‐noising, compensating for environmental variables, and extracting damage signatures. A possible “high‐level” classification arranges the damage detection, localization and quantification approaches in 126 : (i) baseline‐dependent; (ii) baseline‐free; and (iii) instantaneous baseline methods 127 . Another possible classification distinguishes: (iv) statistical‐based (image‐based) 128 ; and (v) machine learning methods 129 .…”

“…A possible "high-level" classification arranges the damage detection, localization and quantification approaches in 126 : (i) baseline-dependent; (ii) baseline-free; and (iii) instantaneous baseline methods. 127 Another possible classification distinguishes: (iv) statistical-based (imagebased) 128 ; and (v) machine learning methods. 129 Modeling and simulation are essential to understand LW interaction with damage and loading inputs, to discern sensor-structure interaction, to find sensors/actuators optimal placement and to tune the diagnostic input parameters.…”

Baseline-free damage detection and sizing under varying temperatures using Lamb waves without temperature compensation

“…It is in contrast with the prevalent intuition that the best reconstruction occurs when only one mode exists. The value of f rc for a structure-transducer system does not vary with the distance between the actuator–sensor pair and can be ascertained from experiments, analytical solutions, 47,48 or FE simulations.…”

On the Directivity of Acoustic Waves Generated by the Angle Beam Wedge Actuator in Thin-Walled Structures

“…The most interesting benefits of using guided Lamb waves is their ability to detect defects in thin-walled structures such as inclusions, porosity, undesirable local changes of the material's mechanical properties, and sometimes a possibility to control the waves directivity, i.e., beamsteering. The aspects of using acoustic waves in the active SHM system are outlined and considered in monographs [1][2][3], in papers [4][5][6][7][8], and in theses [9][10][11][12].…”