Extension of the Shear-Lag Solution for Structurally Attached Ultrasonic Active Sensors

摘要

The objective of this Technical Note has been to understand how ultrasonic excitation is transmitted from a PWAS into a thin-wall structure through the adhesive layer and how it is distributed into the Lamb-wave modes existing in the structure. We recalled the widely cited seminal works by Crawley and deLuis [1] and Crawley and Anderson [2] and we noticed that their applicability is limited to low-frequency applications at which the guided-wave modes are approximated by the axial and flexural waves with their characteristic linear behavior across the thickness. We extended Crawley and deLuis's [1] and Crawley and Anderson's [2] works to nonlinear guided-wave modes. We obtained a closed-form solution for parameter α and observed that this parameter is no longer constant, but varies with the frequency-thickness product. A graph was given of this variation up to the maximum fd value for which only S0 and A0 modes exist. Changes in α of up to 25% were observed, along with redistribution of its S0 and A0 modes contributions. The theory was further extended to the case of two generic guided-wave modes for which a closed-form solution was still possible. For the case of N generic modes, a closed-form solution was no longer possible, but an iterative approach has been considered and will be reported upon in a future communication.