Energy harvesting using a piezoelectric-flexoelectric nanobeam

Flexoelectricity can be defined as an electromechanical coupling between polarization and strain gradient. In contrast with piezoelectricity, flexoelectricity is largely dominant at the nanoscale. Using a developed electromechanical model of a BaTiO₃ nanobeam, we simulate the dynamic behavior of the device when it is subject to a base harmonic excitation representing mechanical vibrations from the environment. The coupled electromechanical model is first derived using the Hamilton’s principle and accounting for the von Karman strain for relatively large displacements and takes into account an initial static displacement due to residual stresses. The Galerkin approximation is used to discretize the space domain for the transverse displacement and the electric potential. The nonlinear dynamic response of the nanobeam and the generated electrical voltage are solved for limit-cycle solutions. The results depicted higher power density generation when the aspect ratio of the nanobeam is varied. It is found that the initial deflection can mitigate the expected performance of the device.