Discrete singular convolution and spectral finite element method for predicting electromechanical impedance applied on rectangular plates

The impedance-based structural health monitoring using piezoelectric wafer-active sensor has been increasingly developed for aerospace, civil, and mechanical structures. Using electromechanical coupling effects of piezoelectric wafer-active sensor, impedance of piezoelectric wafer-active sensor can detect any change in a structure. Piezoelectric wafer-active sensor is embedded and bounded to the structure in order to monitor the structure in a preferred frequency range. This article presented a general model to predict the impedance of piezoelectric wafer-active sensor bounded to a plate structure and also developed a general model for the influence of interaction of piezoelectric wafer-active sensor and plate on the structural response in impedance-based structural health monitoring. To obtain equations of vibrations, in the first step, potential and kinetic energies of fully free Kirchhoff and Mindlin plates with piezoelectric wafer-active sensor are derived. Numerical solutions for structural vibration of the plate developed using discrete singular convolution methods and applied based on Rayleigh-Ritz method in very high frequencies. After calculating mass and stiffness matrices of structure and piezoelectric wafer-active sensor, impedance of piezoelectric wafer-active sensor was determined using piezoelectric constitutive equations. Also, a three-dimensional spectral finite element method was used to model impedance of plate. An experimental setup was used for modal analysis to obtain low natural frequencies and calculate the impedance of piezoelectric wafer-active sensor in high frequencies. Finally, the comparison of numerical results of three-dimensional spectral element method and experimental results verified this model.