A component coupling approach to dynamic analysis of a buckled, bistable vibration energy harvester structure

Over the past ten years, the energy harvesting community has focused on bistable structures as a means of broadening the working frequency range and, by extension, the effective efficiency of vibration-based power scavenging systems. In the current study, a new method is implemented to statically and dynamically analyze a bistable buckled, multi-component coupled structure designed specifically for low-frequency (< 30Hz) vibration energy harvesting. First, the system is divided into its individual components and the governing equations for each part are developed based on Euler-Bernoulli beam theory. These governing equations are then solved in one single system of equations by applying geometrical and force-moment boundary conditions at the connections. Solving the nonlinear static equations gives the critical buckling loads, as well as the exact static, post-buckled configuration of the system about which the dynamic response is formulated. The natural frequencies and mode shapes of the system are obtained by solving the free vibration case of the linearized buckled structure, which are then used as spatial functions in a Galerkin approach to discretize the nonlinear partial differential equations of the coupled system. To validate the modeling approach, the obtained results are compared with the ones captured from both finite element analysis model and the experimental setup, which shows good agreement between them. Furthermore, the amplitude-frequency response of the system and snap-through regime with the variation of various parameters, including exciting frequency, base vibration and buckling loads are investigated based on the developed model. It is shown that for a weakly buckled configuration, bistable motion can be captured for a wide range of frequencies, which is crucial for the performance of energy harvesting devices.