Analytical Approximation and Experimental Study of Bi-Stable Hybrid Nonlinear Energy Harvesting System

The paper presents modeling, analytical investigation and experimental study of a nonlinear hybrid energy harvesting system in the bi-stable configuration. Linear energy harvesters are frequency sensitive meaning they only generate reasonable power if they are excited accurately at their first natural frequency. Nonlinear effects can be used to increase the effective range of excitations frequency by broadening the frequency response. The proposed hybrid energy harvester uses Piezoelectric and Electromagnetic transduction mechanisms. Electromechanical coupling has been included in the study of the nonlinear dynamics of the harvester. The shooting method has been used to numerically calculate the limit cycles of the bi-stable system. The calculated limit cycles and the Poincare map of the system give the big picture of system vibrations due to the base accelerations. An approximation method is suggested using the method of multiple scales and verified by numerical integrations to find an equivalent forced, damped Duffing oscillator for the original harvesting system. The approximation results the equivalent mechanical system that acts similar to the coupled electromechanical harvester. The approximation is a function of the harvesting circuit so the back coupling is not overlooked. Meanwhile the amount of computations and the complexity of the problem are significantly reduced. The nonlinear vibration of the proposed nonlinear bi-stable harvester is also experimentally investigated. The study shows that the Limit Cycle Oscillations of the nonlinear system increase the power production by two orders of magnitude. The relations between the power output and the excitation level, the excitation frequency, and the electric loads are investigated.