An electromechanical impedance approach for quantitative damage detection in Timoshenko beams with piezoelectric patches
As a qualitative health monitoring method, the electromechanical impedance technique ( EMI) has been widely studied. Due to the complexities of the damaged structures and the difficulties in high-frequency analysis, further information about the nature of damage cannot be obtained using EMI in its conventional non-model-based way. Thus, in this paper, a hybrid technology combining the EMI technique and reverberation matrix method (RMM) is proposed to quantitatively correlate damage in beam structures with high-frequency signatures for structural health monitoring. Timoshenko beam theory is employed to study the dynamics of beam-like structures bonded with multiple pairs of PZT patches. A piecewise, homogeneous beam model is introduced to approximate the nonhomogeneous beam in which inhomogeneity is introduced because damages of an originally uniform beam can be modeled by different cross-sectional properties. Here, only one-dimensional axial vibration of PZT wafers is considered. A shear lag model is adopted to simulate the interfacial bonding between PZT patches and the host beam. An analytical expression of impedance ( or admittance) related to the response of the coupled model of the PZT patch-bonding layer-host beam system is derived and then investigated by comparing with other theories. Finally, covariance, a kind of non-parametric damage index, is also employed to identify the damage severity, propagation and location.