Nonlinear dynamic analysis of asymmetric bistable energy harvesters

Nonlinear vibration energy harvesting systems can potentially increase the power collected from the kinetic energy available in their operating environment since they usually can recover energy in broadband frequencies compared to their linear counterpart. However, these systems have a high degree of complexity, sensitivity to slight variations of the parameters and the initial conditions, and may present multiple solutions. For these reasons, it is rare for the designer to have a deep understanding of the dynamic behavior of this type of nonlinear oscillator. This situation is even more peculiar when geometric imperfections from the system's manufacturing process are present, as they can significantly influence the energy recovery process. Intending to fill this lack of understanding about general aspects of the nonlinear dynamics of this kind of system, the present paper presents a broad numerical investigation of local and global characteristics of the underlying dynamical systems using bifurcation diagrams and basins of attraction. Bifurcation analysis is performed by exploring the broad spectrum of a harmonic signal, going from low to high amplitude and frequency of excitation. Basins of attraction analysis based on 0-1 test for chaos is proposed as an efficient statistical technique to identify chaotic and periodic solutions. Different levels of asymmetry are investigated, and a particular situation is defined and analyzed when a value of the sloping angle where the system is attached compensates for the asymmetry of the quadratic term. The result shows the different solutions defined by excitation forces and initial conditions, indicating the best scenario for increasing the power output. The adverse effects of the asymmetries are presented. However, we also demonstrated that it is possible to around this behavior using the sloping angle to compensate for the asymmetric influence