Structural health monitoring (SHM) of structures by electromechanical impedance (EMI) technique using non-linear material model of piezoelectric medium

Abstract

Piezoelectric materials because of direct and converse effects are used both as sensors and actuators. The electromechanical impedance characteristics of the piezoelectric materials are utilized for diagnosing health of the structures. The electromechanical impedance (EMI) technique is employed in the frequency range of 30 to 400 kHz. In the EMI technique, a piezoelectric patch is bonded to the surface of the monitored structure using a high strength epoxy adhesive and electrically excited via an impedance analyzer. The response of the structure is captured through another piezoelectric patch bonded on the structure and acting as sensor. In such situation, the piezoelectric patch can be modelled as undergoing axial vibration and interacting with the host structure. The one-dimensional vibration of piezoelectric patch is governed by one-dimensional wave equation derived based on dynamic equilibrium of piezoelectric patch. A first principle based modelling of non-linear constitutive relation of piezoelectric medium is presented. Non-linear material property is implemented in the wave equation to obtain non-linear wave equation. Material non-linearity gives rise to an internal source term in the non-linear wave equation. This non-homogeneous wave equation is solved by Green's function approach. This modelling is further implemented for evaluation of its response in structural health monitoring application. Equilibrium condition of the piezoelectric patch is established by considering inertia and stiffness effects. Expression for current in piezoelectric patch is obtained from electric displacement equation. Henceforth electromechanical impedance expression is derived. Electromechanical admittance is the inverse of the electromechanical impedance. The real part of the admittance is the conductance and the imaginary part of admittance is the susceptance. The variation of conductance and susceptance with respect to frequency is plotted. © 2017 International Center for Numerical Methods in Engineering. All rights reserved.