Three-dimensional formulation of a strain-based geometrically nonlinear piezoelectric beam for energy harvesting

In this paper, the authors introduce a model of a strain-based geometrically nonlinear piezoelectric beam for modeling energy harvesters. A nonlinear shear-underfomable 3-D Rayleigh’s beam theory is used to model the displacement fields and can be considered as an interesting alternative to linear and highly nonlinear models commonly presented in the literature. The nonlinearities are introduced to reproduce the behavior of the flexible structure, since moderate to large displacements can occur in response of external loading conditions. The finite element method is used to model the piezolaminated bimorph configuration. Each finite element consists of two piezoelectric energy harvesters embedded or perfectly bonded to an elastic substrate. The electromechanical coupling includes axial and flexural effects as well as additional term that comes from the nonlinearity incorporated into the strain tensor. Additionally, the authors explore briefly two topics for linear harvesters: the influence of the electric domain on the structural properties and, the performance of the harvester near resonance in term of electric power output of a purely resistive network. As a validation case, a cantilevered piezoelectric energy harvester under base excitation is modeled. Alongside, the response to gust of a harvester embedded in a wing structure is analyzed.