Investigation Of The Piezoelectric Energy Harvesting Under Random Excitations

The concept of vibratory energy harvesting has flourished in recent years as a possible alternative to provide a continuous power supply.Compared with linear energy harvesters' resonant counterparts,bistable nonlinear energy harvesting has a wider steady-state frequency bandwidth,which can be utilized to improve performance in ambient environments.Nonlinear bistable energy harvesting has become a prominent research endeavor,owing to both its broad frequency range and harvesting efficiency.In the paper,the dynamical model of piezoelectric bistable cantilever beam and dynamic equation are established according to the large deflection vibration properties of the bistable piezoelectric vibrator.The efficiency of the energy harvesting is analyzed by using four dimensional nonlinear differential equations under random excitation.Firstly,the derivation method of transverse mode function of the uniform Euler-Bernoulli beams and the free boundary conditions are used to obtain the analytic expression of vibration mode function of the Euler-Bernoulli beams with step changes in cross section.Then,the Lagrange function of the system is established based on piezoelectric vibration theory,magnetic theory,and mode transformation method for the uniform cantilever beam,considering the influence of environmental random excitation.Considering three dimensional vibration mode function of Euler-Bernoulli beams with step changes,the separation of variables is carried out by the Galerkin's Process.Subsequently,the four dimensional ordinary differential equations of the bistable cantilever beam energy harvesting is established based on Hamilton principle.And the dimensionless equations are obtained.Finally,the bistable piezoelectric system is simulated numerically,the time history,phase diagram,frequency spectrum and Poincare mapping diagram under various excitation are shown,and the nonlinear behavior of the bistable piezoelectric harvesting system is analyzed.And the efficient of the equipment harvesting energy is demonstrated by the average power value diagram.