Design Optimization of Linear and Non-Linear Cantilevered Energy Harvesters for Broadband Vibrations

In much of the vibration-based energy harvesting literature, resonant energy harvesters are designed around a single base excitation frequency, whereas many applications comprise broadband, time-varying vibrations. Since many naturally occurring vibrations are low frequency, a relatively large mass or beam length is required to resonate at the driving frequencies. This article presents a modeling and optimization procedure for designing vibration energy harvesters for maximizing power generated by vibrations recreated from real-world sources at low frequencies. It is shown that the device coupling coefficient, a significant parameter in determining the energy transduction performance, can be decoupled into terms related to the stiffness and mass distribution of the device, each of which can be optimized independently. To demonstrate the use of this design optimization procedure, measured accelerations are used to provide time-varying, broadband inputs to the energy-harvesting system. Under various size and mass constraints, optimal linear resonant harvesters are presented for human walking and automobile driving scenarios. The frequency response functions are presented alongside time histories of the power harvested using the experimental base acceleration signals. Finally, these results are compared to a non-linear device that utilizes spatially periodic magnetic excitation, a feature that is particularly suited to low-frequency, time-varying excitation.