Hysteretic Nonlinear Characteristics and Stochastic Bifurcation of Cantilevered Piezoelectric Energy Harvester

摘要

Hysteretic nonlinear characteristics and stochastic bifurcation of cantilevered piezoelectric energy harvester was studied in this paper. Piezoelectric ceramics was adhesively bonded on the substrate of cantilever beam to make piezoelectric cantilever beam. Von de Pol difference item was introduced to interpret the hysteretic phenomena of piezoelectric ceramics, and then the nonlinear dynamic model of piezoelectric cantilever beam subjected to axial stochastic excitation was developed. The stochastic stability of the system was analyzed, and the steady-state probability density function and the joint probability density function of the dynamic response of the system were obtained. Finally, the conditions of stochastic Hopf bifurcation were determined. Numerical simulation shows that stochastic Hopf bifurcation appears when bifurcation parameter varies, which can increase vibration amplitude of cantilever beam system and improve the efficiency of piezoelectric energy harvester. The results of this paper are helpful to application of cantilevered piezoelectric energy harvester in engineering fields.