Constrained Design Optimization of Vibration Energy Harvesting Devices

Existing design criteria for vibration energy harvesting systems provide guidance on the appropriate selection of the seismic mass and load resistance. To harvest maximum power in resonant devices, the mass needs to be as large as possible and the load resistance needs to be equal to the sum of the internal resistance of the generator and the mechanical damping equivalent resistance. However, it is shown in this paper that these rules produce suboptimum results for applications where there is a constraint on the relative displacement of the seismic mass, which is often the case. When the displacement is constrained, increasing the mass beyond a certain limit reduces the amount of harvested power. The optimum load resistance in this case is shown to be equal to the generator's internal resistance. These criteria are extended to those devices that harvest energy from a low-frequency vibration by utilizing an interface that transforms the input motion to higher frequencies. For such cases, the optimum load resistance and the corresponding transmission ratio are derived.