Stiffness control of a nonlinear mechanical folded beam for wideband vibration energy harvesters

This paper presents a novel approach to design and optimize geometric nonlinear springs for wideband vibration energy harvesting. To this end, we designed a spring with several folds to increase its geometric nonlinearities. A numerical analysis is performed using the Finite Element Method to estimate its quadratic and cubic spring stiffness. A nonlinear effective spring constant is then calculated for different values of the main folding angle. We demonstrate that this angle can increase nonlinearities within the structure resulting in higher bandwidths, and that it is possible to control the behavior of the system to have softening-Type or hardening-Type response depending on the choice of the folding angle. Based on the Lindstedt-Poincaré perturbation technique, a first order approximation is determined to predict the frequency-response of the system. In order to validate the perturbation analysis, numerical solutions based on long-Time integration method and mixed VHDL-AMS/Spice simulations are presented. Finally, this method is applied to a previously published device and shows a good agreement with experiments.