Search

This paper focuses on global dynamic behaviors of a bistable piezoelectric cantilever energy harvester with a tip magnet and a single external permanent magnet at the near side. The initial distance between the magnetic tip mass and the external magnet is altered as a key parameter for the enhancement of the energy harvesting performance. To begin with, the dynamical model is established, and the equilibria as well as potential wells of its non-dimensional system are discussed. Three different values of the initial distance are selected to configure double potential wells. Next, the saddle-node bifurcation of periodic solutions in the neighborhood of the nontrivial equilibria is investigated via the method of multiple scales. To verify the validity of the prediction, coexisting attractors and their fractal basins of attraction are presented by employing the cell mapping approach. The best initial distance for vibration energy harvesting is determined. Then, the Melnikov method is utilized to discuss the threshold of the excitation amplitude for homoclinic bifurcation. And the triggered dynamic behaviors are depicted via numerical simulations. The results show that the increase of the excitation amplitude may lead to intra-well period-2 and period-3 attractors, inter-well periodic response, and chaos, which are advantageous for energy harvesting. This study possesses potential value in the optimization of the structural design of piezoelectric energy harvesters. [ABSTRACT FROM AUTHOR]

The investigation of global bifurcation behaviors the vibrating structures of micro-electromechanical systems (MEMS) has received substantial attention. This paper considers the vibrating system of a typical bilateral MEMS resonator containing fractional functions and multiple potential wells. By introducing new variations, the Melnikov method is applied to derive the critical conditions for global bifurcations. By engaging in the fractal erosion of safe basin to depict the phenomenon pull-in instability intuitively, the point-mapping approach is used to present numerical simulations which are in close agreement with the analytical prediction, showing the validity of the analysis. It is found that chaos and pull-in instability, two initial-sensitive phenomena of MEMS resonators, can be due to homoclinic bifurcation and heteroclinic bifurcation, respectively. On this basis, two types of delayed feedback are proposed to control the complex dynamics successively. Their control mechanisms and effect are then studied. It follows that under a positive gain coefficient, delayed position feedback and delayed velocity feedback can both reduce pull-in instability; nevertheless, to suppress chaos, only the former can be effective. The results may have some potential value in broadening the application fields of global bifurcation theory and improving the performance reliability of capacitive MEMS devices. [ABSTRACT FROM AUTHOR]

Global dynamics of a piezoelectric energy harvester with tristable potential is investigated. The dynamical model of a cantilever beam energy harvester is considered; its static bifurcation is also discussed. Multiple intra-well attractors and their basins of attraction are presented to discuss the mechanism of multistability and its initial sensitivity. Moreover, the Melnikov method is applied to present the conditions for global bifurcations and the induced complex dynamics. The results show that the variation of coefficients of the polynomial may affect the number and shapes of potential wells, while the increase of the excitation amplitude may trigger multistability around one equilibrium, initial-sensitive jump, inter-well attractor and chaos. The results may provide some theoretical reference for increasing the working performance of energy harvesters. [ABSTRACT FROM AUTHOR]