Modeling of Static Stress Identification Using Electromechanical Impedance of Embedded Piezoelectric Plate

Working stress is an important indicator reflecting the health status of structures. Passive-monitoring technology using the piezoelectric effect can effectively monitor the dynamic stress of structures. However, under static loads, the charge generated by the piezoelectric devices can only be preserved when the external circuit impedance is infinitely large, which means passive-monitoring techniques are unable to monitor static and quasi-static stress caused by slow-changing actions. In current studies, experimental observations have shown that the impedance characteristics of piezoelectric devices are affected by external static loads, yet the underlying mechanisms remain inadequately explained. This is because the impedance characteristics of piezoelectric devices are actually dynamic characteristics under alternating voltage. Most existing impedance analysis models are based on linear elastic dynamics. Within this framework, the impact of static stress on dynamic characteristics, including impedance characteristics, cannot be addressed. Accounting for static stress in impedance modeling is a challenging problem. In this study, the static stress applied on an embedded piezoelectric plate is abstracted as the initial stress of the piezoelectric plate. Based on nonlinear elastic dynamic governing equations, using the displacement method, an impedance analysis model of an embedded piezoelectric plate considering initial stress is established and verified through a fundamental experiment and a finite element analysis. Based on this, the explicit analytical relation between initial stress and impedance characterizations is provided, the mechanism of the effect of initial stress on the impedance characterizations is revealed, and procedures to identify static stress using impedance characterizations is proposed. Moreover, the sensitivities of the impedance characterizations in response to the initial stress are thoroughly discussed. This study mainly provides a theoretical basis for monitoring static stress using the electromechanical impedance of an embedded piezoelectric plate. And the results of the present study can help with the performance prediction and design optimization of piezoelectric-based static stress sensors.