Analytical modeling, simulation and experimental study for nonlinear hybrid piezoelectric–electromagnetic energy harvesting from stochastic excitation

For the designed nonlinear hybrid piezoelectric (PE)–electromagnetic (EM) energy harvester, electromechanical coupling state equations are established at stochastic excitation, and vibration response, output mean power, voltage and current are derived by statistical linearization method. Then, effects of nonlinear strength, load resistance and excitation spectral density on vibration response and electric output of nonlinear hybrid energy harvester are studied by theoretical analysis, simulation and experimental test. It is obtained that mean power of nonlinear hybrid energy harvester increases linearly with acceleration spectral density; the bigger nonlinear strength, the bigger output power of energy harvester and the lower resonant frequency are; besides, mean amplitude of nonlinear hybrid energy harvester reaches the minimum at PE optimal load, but it increases with EM load increasing. Compared with linear hybrid energy harvester, the resonant frequency of nonlinear energy harvester can be decreased by 57%, while output power can be increased by 72%.