Detecting period-doubling bifurcation routes to chaos in a vibro-impact piezoelectric energy harvester

Abstract Recently, ambient vibration energy harvesters as power supplies for small-scale electronic devices or wireless sensor networks have attracted great research interest. Equipping vibration energy harvesters with mechanical stoppers can not only provide an auto-protection mechanism, but also increase the effective frequency bandwidth due to the vibro-impact feature. However, because of the nonlinear contact forces and, consequently, complex nonlinear responses, designing the rectifier circuits becomes more complicated with this type of design. So, a novel vibro-impact piezoelectric energy harvester is presented in this paper. Lagrange’s equations and Kirchhoff’s voltage law are used to derive the electromechanical equations. The numerical tools, including phase portraits, bifurcation diagrams, Fourier spectrum, Poincaré sections and Lyapunov exponents are utilized to scrutinize the effects of the excitation frequency and the gaps between the stoppers and the lumped masses on the formation of chaotic regions in the response of the harvester. A prototype is fabricated and tested to validate the theoretical results. The results indicate that the higher gap values lead to wider range of chaotic responses. Also, the chaotic responses are more frequently observed for the asymmetric stopper configuration. In addition, a peak voltage of 9.4 V at a resonant frequency of 29 Hz is shown in experiments for a base acceleration of 0.1 g and the asymmetric configuration. Results of this paper give better insight into problem of nonlinear dynamics of vibro-impact piezoelectric energy harvesters.