Quantitative structural damage detection using high‐frequency piezoelectric signatures via the reverberation matrix method

High-frequency structural analysis so far has been a major issue in dynamic analysis, for which many conventional methods such as finite element method and transfer matrix method are unable to perform well. Since the electromechanical impedance technique for structural health monitoring (SHM) operates at very high frequencies, the reverberation matrix method (RMM), which was just developed a few years ago, is employed to study dynamics of the monitored structures, which are bonded with piezoelectric lead zirconate titanate (PZT) patches. A piecewisely homogeneous Euler–Bernoulli beam model is introduced to approximate the non-homogeneous beam and only one-dimensional axial vibration of PZT wafers is considered. The imperfect interfacial bonding between PZT patches and the host beam is investigated based on a shear lag model. Using a hybrid technique combining electromechanical impedance method and RMM, an analytical expression of impedance (or admittance) related to the response of the coupled model of PZT patch-bonding layer-host beam system is derived for SHM. The proposed method is examined by comparing with other theoretical methods as well as by means of a test on an intelligent system using a steel beam with two symmetrically installed PZT wafers. It could be further applied to predicting the dynamics of monitored Timoshenko beams, continuous beams, and framed structures as well. Copyright © 2006 John Wiley & Sons, Ltd.