Nonlinear Dynamic Modeling and Optimum Electric Power Determination in Energy Harvesting by Bimorph Piezoelectric Cantilever

In recent years, researches on energy harvesting by piezoelectric ceramics have increased. Generally, linear electromechanical constitutive equations have been utilized to model the behavior of piezoelectric based harvester. But, the linear modeling shows erroneous output for high amplitude and frequency inputs. In these cases, due to nonlinear material behavior, the nonlinear modeling should be carried out. In this paper, the nonlinear behavior and optimum response of a symmetric bimorph cantilever under the base excitation is studied. Electromechanical formulation is based on the Euler-Bernoulli beam theory. A proposed nonlinear enthalpy is used to model the nonlinear dynamic using Lagrange equations. Applying the multiple scale perturbation method, the nonlinear coefficients are identified experimentally (μ ̅_1=3.0090×〖10〗^16 and _1=-4.5804×〖10〗^20 ). Then, nonlinear behavior of harvester has been analyzed considering generated voltage, current and beam deflection. Finally, using the results of Power FRF, the optimum load resistance is achieved to maximize the generated power (R_l=177.828 kΩ).