Nonlinear analysis of unimorph and bimorph piezoelectric energy harvesters with flexoelectricity

This work investigates the nonlinear behaviors of nanoscale unimorph and bimorph piezoelectric energy harvesters under harmonic base excitations. In the modeling, the energy harvesters are based on cantilevered beams with tip mass, and the effects of geometric nonlinearity, inertial nonlinearity and flexoelectricity are considered. Based on the Hamilton's principle and the theory of flexoelectricity, the nonlinear coupled governing equations of the system are derived. Galerkin's method is employed to discrete the nonlinear equations, which are then numerically solved. Results indicate that geometric nonlinearity leads to a typical hardening nonlinear behavior of the frequency response curve while inertial nonlinearity leads to a softening behavior in contrast. In addition, influences of the tip mass and amplitude of the base acceleration on the harvesters' electrical outputs are examined. By comparing lead zirconate titanate (e.g. PZT-5H) and polyvinylidene difluoride (i.e. PVDF) as the material for piezoelectric layers, it is found that the performance enhancement of PVDF energy harvester due to flexoelectricity is more prominent. It is also interesting to observe the flexoelectricityinduced size-dependent voltages. This work compares the performance of energy harvesters with various structures and materials, which will provide guidance for the design and optimization of piezoelectric energy harvesters utilizing flexoelectricity.