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

Document Type


Subject Area(s)

Engineering, Mechanical Engineering


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.