Modeling of EMI response of damaged Mindlin–Herrmann rod

To ensure high sensitivity to incipient damages, electromechanical impedance (EMI) is measured at high frequencies for damage detection. In the working high-frequency range, very high vibration modes, of the order of the thousandth mode or higher, of a structural member are likely to be activated. This imposes a great difficulty on the accurate modeling of EMI response of a structure. In this paper, the reverberation matrix method (RMM) is adopted to study the dynamics of a Mindlin–Herrmann rod with surface piezoelectric patches. The rod is inhomogeneous along the axial direction so that damage-induced reduction of cross-section or Young's modulus could be easily incorporated in the model. A piecewise-homogeneous rod model is subsequently introduced to approximate the inhomogeneous rod, along with a shear lag model of interfacial bonding between the lead zirconate titanate (PZT) patches and the host rod. An analytical expression for the electric impedance (or admittance) of the coupled model of PZT patch-bonding layer-host rod system is derived. Comparison with other established results is presented. Parametric investigations are also performed to show the dynamic properties of the coupled smart structural system. The analysis in this paper provides necessary theoretical basis for damage detection of rod via the EMI signatures.