A comprehensive dynamic continuous model of piezoelectric stack energy harvesters under arbitrary excitation considering electrodes and protective layers

Piezoelectric stack energy harvesters, by virtue of the higher mechanical-to-electrical energy conversion capability in the d 33 mode, have been used widely in various fields, such as railway system, roadway system, and human motion. Dynamic continuous models (DCMs) of piezoelectric stack energy harvesters can more accurately reflect the electromechanical behavior but are difficult to be established due to complex coupling between layers, particularly in the presence of arbitrary loads. The existing models often only considered harmonic excitations and often ignored electrodes and protective layers for simplicity. This paper proposed a comprehensive DCM of piezoelectric stack energy harvesters considering the electrodes and protective layers, which can be used to study the electromechanical performance of the energy harvester under both harmonic excitation and arbitrary excitation. Comparisons of the developed generic DCM with the analytical model based on piezoelasticity theory (a DCM which only considers the harmonic excitation) and the simplified model (a quasi-static continuous model which ignores inertia force of piezoelectric stack) are presented, with good agreements. Furthermore, the experiment results of two shapes of piezoelectric stacks, including tube and circular, are used to further confirm the reliability of the proposed model. In addition, effects of the electrode and protective layers on the dynamic properties are analyzed and discussed. The results show that the proposed DCM is effective and versatile to guide the design of piezoelectric stack energy harvesters subject to various types of loads.