In this paper, a mathematical model for a Piezoelectric plate which is used for harvesting the energy from nonlinear transverse vibration has been presented. For this purpose, at first, nonlinear equation of motion of the PZT plate have been derived based on the Kirchhoff plate theory. Then, the equivalent electrical circuit of the structures is developed. These equations have been reduced to some ordinary deferential equations (ODE) using Airy stress function and Galerkin Method. Using Method of Multiple scales (MMS), an analytical solution has been done and a closed form relation for the output power of harvester has been obtained. To validate the obtained results from these relations, a FE Modeling using COMSOL Multiphysics has been made and a good agreement between FEM results and numerical solution of the mathematic model for displacement and voltage have been shown. After validation, to extract the maximum power, introducing analytical relation for the power as cost function, an optimization for extracting the best parameters of the harvester to obtain the maximum power has been done using Genetic Algorithm method. Also, the effect of various parameters of the structure such as dimension and thickness on the power have been investigated.
