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Typically, the Electromechanical Impedance (EMI) technique does not use an analytical model for basic damage identification. However, an accurate model is necessary for getting more information about any damage. In this paper, an EMI model is presented for predicting the electromechanical impedance of a cracked beam structure quantitatively. A coupled system of a cracked Timoshenko beam with a pair of PZT patches bonded on the top and bottom surfaces has been considered, where the bonding layers are assumed as a Kelvin-Voigt material. The shear lag model is introduced to describe the load transfer between the PZT patches and the beam structure. The beam crack is simulated as a massless torsional spring; the dynamic equations of the coupled system are derived, which include the crack information and the inertial forces of both PZT patches and adhesive layers. According to the boundary conditions and continuity conditions, the analytical expression of the admittance of PZT patch is obtained. In the case study, the influences of crack and the inertial forces of PZT patches are analyzed. The results show that: (1) the inertial forces affects significantly in high frequency band; and (2) the use of appropriate frequency range can improve the accuracy of damage identification.

The analytical model of pulsed eddy current (PEC) serves as a tool to explore the detection mechanism of PEC testing, which is widely used to optimise the design of probes and analyse the influence on PEC signals. However, based on the analytical model of impedance change, the computational efficiency of the PEC model for pipelines is low at present, which means that a lot of time is consumed and the application of the analytical model of PEC is suppressed. In order to improve the efficiency of numerical calculation, this paper proposes a fast numerical calculation method for the analytical model of PEC for pipelines, based on the integral model of impedance change. Firstly, in order to improve the calculation efficiency of the Dodd and Cheng model, this paper reveals that the generalised integral can be changed into a definite integral by studying the properties of the integral function. Secondly, according to the partial derivative characteristic of impedance change with frequency, the method of piecewise cubic spline interpolation is used to calculate the impedance change of harmonics. Finally, an analytical model of PEC for single-layer pipeline is calculated and the results are compared with the finite element method (FEM) to verify the accuracy and efficiency of the proposed method. The results indicate that the method could be used to improve the computational efficiency of the PEC model for pipelines when only conductivity is changed.

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