Exact Shear-Lag Solution for Guided Waves Tuning with Piezoelectric-Wafer Active Sensors

This paper addresses some unresolved predictive modeling issues related to the use of piezoelectric-wafer active sensors for ultrasonic structural health monitoring. An exact model for the shear-lag transfer between the piezoelectric-wafer active sensor transducer and the structure in the presence of N generic guided wave modes is derived from first principles using the normal-mode expansion formulation. The resulting integral differential equation is solved using the variational iteration approach. The resulting solution is used to derive an improved model for the tuning between piezoelectric-wafer active sensor transducers and the multimodal guided waves used in ultrasonic structural-health-monitoring applications. The numerical predictions generated by the improved tuning model are compared with experimental results obtained through pitch catch experiments between two 7 mm piezoelectric-wafer active sensor transducers placed on a 1-mm 2024-T3 aluminum plate. The 10-700 kHz frequency range was explored. It was concluded that the improved model using the exact shear-lag solution matches much better the experimental results than previous models. Further theoretical and experimental work is warranted as a follow-up on the work reported in this paper to study the accuracy and convergence properties of the solution, to explore experimental comparison beyond the A1-mode cutoff frequency, and to extend the approach to layered structures and composite materials.