Damage indication in smart structures using modal effective electromechanical couplingcoefficients

Abstract

This work explores the use, in structural health monitoring, of the so-called modal effectiveelectromechanical coupling coefficient (EMCC) as a damage indicator for structures withfailures such as cracks. For this purpose, a discrete layered finite element (FE) modelfor smart beams is proposed and applied to short-circuit (SC) and open-circuit(OC) modal analyses of healthy and damaged (cracked) cantilever beams withsymmetrically surface-bonded piezoelectric patches. Focus is made here on enhancing theelectrical behavior modeling by introducing a quadratic bubble function in theelectric potential through-the-thickness approximation. Therefore, the correspondinghigher-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-orderinduced potential (HIP); then the physical equipotential (EP) electrode effect, oftenneglected 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 andOC-based EMCC change factors (ECFs) and frequency change factors (FCFs) interms of the crack depth and position ratios. It was found that the EP effectwas more influential on the ECF than the SE. However, for the FCFs, the EPeffect was influential only when it is defined from the OC frequencies. Finally, theECFs were found to be higher than the FCFs, in particular for higher modes.