Modeling of geometric, material and damping nonlinearities in piezoelectric energy harvesters

The performance of piezoelectric energy harvesters (PEHs) operating in the anticipated vibration environments depends upon various nonlinearities existing in electromechanical dynamic system. In this paper, the influence of geometric, material and damping nonlinearities on the dynamic response of PEH is investigated. So far, the nonlinear geometric finite element analysis has not been used for analyzing PEHs. Moreover, the criterion for inclusion/exclusion of geometric nonlinearity in analyzing PEHs is not studied in detail. In this paper, firstly, the finite element modeling is used for analyzing the effect of geometric nonlinearity for low-frequency vibration sources. Simulations are carried out using ANSYS for different PEH configurations to assess the influence of geometric nonlinearity on harvester's performance, and a parameter is proposed to determine the inclusion/exclusion of geometric nonlinearity in the analyzing PEHs. Subsequently, a nonlinear electromechanical model considering material and damping nonlinearities is derived for a cantilever-type PEH which uses macro-fiber composite (MFC) for power generation. In the earlier works on PZT-5A and PZT-5H, the nonlinear elastic and damping coefficients were identified by matching the analytical responses (e.g., voltage or displacement) with a set of experimental responses, which is an indirect method and might result in erroneous estimation of unknown coefficients as pointed out in the present work. In this study, the material behavior of MFC is directly obtained from tensile tests. The observed nonlinear stress-strain behavior of MFC is included in the nonlinear model to study the dynamics of the harvester. Energy harvesting experiments are conducted, and the harvester's response is compared with the predictions from the proposed nonlinear model. The comparison shows very good agreement between the experimental and predicted responses. Moreover, the damping parameters are identified using the energy balance method, and it is shown that nonlinear damping is essential in accurate modeling of PEHs.