Damage indication in smart structures using modal effective electromechanical coupling coefficients

摘要

This work explores the use, in structural health monitoring, of the so-called modal effective electromechanical coupling coefficient (EMCC) as a damage indicator for structures with failures such as cracks. For this purpose, a discrete layered finite element (FE) model for smart beams is proposed and applied to short-circuit (SC) and open-circuit (OC) modal analyses of healthy and damaged (cracked) cantilever beams with symmetrically surface-bonded piezoelectric patches. Focus is made here on enhancing the electrical behavior modeling by introducing a quadratic bubble function in the electric potential through-the-thickness approximation. Therefore, the corresponding higher-order potential (HOP) degree of freedom is condensed at the ply level, leading to a passive stiffening effect (SE) similar to the so-called higher-order induced potential (HIP); then the physical equipotential (EP) electrode effect, often neglected in the piezoelectric FE literature, is here implemented after the electrodes' FE assembly. After its validation against available analytical and experimental results, the proposed piezoelectric FE is used for parametric analyses of SC-based and OC-based EMCC change factors (ECFs) and frequency change factors (FCFs) in terms of the crack depth and position ratios. It was found that the EP effect was more influential on the ECF than the SE. However, for the FCFs, the EP effect was influential only when it is defined from the OC frequencies. Finally, the ECFs were found to be higher than the FCFs, in particular for higher modes.