Electromechanical impedance modeling of cantilever beams with embedded PZT transducers

Impedance based Structural Health Monitoring “ISHM” using piezoelectric materials “PZT” has turned into one of the powerful nondestructive evaluation techniques during the last few years. In this field, many works have been done experimentally but a few researches have been focused on theoretical modeling. In this paper, a new model of system based on interaction between structure and PZT as actuator and sensor respectively has been proposed and applied to obtain electrical impedance and natural frequencies of a structure. A cantilever beam has been studied and modeled by Euler-Bernoulli related equations. The strain and kinematic energy of both beam and PZT as actuator have been calculated using model of whole system in which the mass and stiffness matrices of beam and PZT are integrated. This model provides a continuous classical theoretical approach to solve the dynamic equations of the system different from previous models. The numerical results of the model have been calculated using Rayleigh-Ritz method. Then the related equations of PZT as sensor have been implemented to obtain output electrical impedance of PZT. The experimental results have been carried out using an evaluation board AD5933 on an aluminum cantilever beam to validate our theoretical results including electrical impedance and system natural frequencies. The comparison between theoretical and experimental results shows a good agreement and the proposed theoretical model can be served as a suitable tool in ISHM modeling.