Modeling of elastic, electromechanical coupling and damping nonlinearities for cantilever beam piezoelectric energy harvesters

Piezoelectric energy harvesters (PEHs) exhibit nonlinear behavior due to the inherent nonlinear properties of piezoelectric materials and display a highly damped response. In this article, we experimentally and analytically investigate the material and damping nonlinearities of cantilever beam PEHs. A nonlinear model for piezoelectric cantilever is introduced, incorporating higher-order elastic nonlinearities, electromechanical coupling nonlinearities and nonlinear damping. The nonlinear damping is attributed to structural dissipation, electromechanical conversion and dielectric losses. The method of multiple scales is employed to derive an analytical solution for the nonlinear governing equations, which facilitates the calculation of material nonlinearity coefficients and damping parameters through curve-fitting methods. The model shows good agreement with experimental results and is subsequently used to study PEH performance over a wide range of load resistances and base acceleration levels, revealing that material nonlinearity and damping parameters critically influence the optimal load resistance and resonance frequency of the piezoelectric cantilever.