Bifurcations analysis of a multiple attractors energy harvesting system with fractional derivative damping under random excitation

The multiple attractors energy harvester, which can convert mechanical energy into electrical energy, is a typical birhythmic system. This paper investigates the stochastic bifurcation of the system with fractional derivative damping under different noise excitations. Variable transformation and conversion mechanism for decoupling the electromechanical equations are utilized to obtain the approximate equivalent system. Probability density functions of the system are generated via the stochastic averaging method. Numerical results are presented to verify the effectiveness of the method. In the deterministic case, the fractional order can effectively control the birhythmic properties. In the stochastic case, the effects of fractional derivative damping and different noises on the stochastic P-bifurcations of the system are discussed separately. It concludes that appropriately changing noise parameters and fractional derivative parameters can increase the harvested energy from vibrations. This study highlights the theoretical contribution in energy harvesting and hopes to provides ideas for optimizing the energy harvesting performance.