Nonlinear model for piezoelectric energy harvester with magnetic coupling

To establish the dynamical model of piezoelectric energy harvester with magnetic coupling, the modeling approach for the harvester is proposed based on nonlinear polynomial description of nonlinear restoring force. The nonlinear restoring force of the cantilever beam being in different positions is measured directly by a small electronic dynamometer and the polynomial parameters of the force are estimated. Then the nonlinear restoring force is taken into account to establish the nonlinear model following Hamilton principle, Euler-Bernoulli beam theory and piezoelectric theory. Runge-Kutta method is introduced to simulate the nonlinear output characteristics of the harvester. The results show that the proposed model enables to simply solve the parameters, reduce calculation task and avoid the direct calculation of magnetic force. And the model can describe the important designing parameters in terms of the jump frequency, maximum voltage and effective bandwidth for the mechanism analysis of magnetic coupled piezoelectric energy harvester.