Nonlinear design and optimisation of a vibration energy harvester

Nonlinear behavior has been exploited over the last decade towards improving the efficiency of most engineering systems. The effect of nonlinearities on a vibration energy harvester (VEH) has been widely studied. It has been reported in literature that a cubic damping nonlinearity extends the dynamic range (power/energy level) of a VEH system. It has also been widely shown that the operational bandwidth of a VEH system can be increased using a nonlinear hardening spring. As most energy harvesters have a maximum throw limited by the physical enclosure of the device, it is imperative to improve the operational conditions of the harvester within this limitation. This paper investigates the effects of a nonlinear hardening spring with cubic damping on a VEH system while assuming no limitation to the maximum throw (Practical VEH systems are constrained to a maximum throw and this is considered in a subsequent study). A frequency-based approach known as Output Frequency Response Function (OFRF) determined using the Associated Linear Equations (ALEs) of the nonlinear system model is employed. The OFRF polynomial is a representation of the actual system model hence used for the nonlinear VEH analysis and design. Based on the OFRF, optimal parameter values are designed to achieve any desired level of energy for the VEH.