Broadband vibration energy harvesting using nonlinear multi degree-of-freedom mechanical filters

We introduce the model of a networked energy harvester for random ambient vibrations, made of mechanically coupled oscillators. The networked harvester is equivalent to a mechanical filter, and it can be modeled as a chain of masses, coupled pairwise by nonlinear elastic springs. Ambient mechanical vibrations are modeled as a low-pass filtered white Gaussian noise, and a piezoelectric transducer is used to convert mechanical kinetic energy into electrical energy. We derive the nonlinear equations of motion for the harvester, together with formulas for the average harvested power and power efficiency. An approximate analytical solution is presented and compared with numerical simulations. Finally, we discuss the optimization of the networked harvester, based on a gradient ascent algorithm combined with Nesterov’s momentum method. We show that, after proper optimization, the mechanically coupled energy harvester scavenges more power than a single mass-spring energy harvester.