Analysis and Optimization of a Multi-Degree-of-Freedom Energy Harvester for Mechanical Vibrations Based on Coupled Resonators

This work describes a model for multi-degrees-of-freedom energy harvesters for ambient mechanical vibrations, based on coupled resonators that form a networked structure. The governing equations of motions for the model are derived, and stochastic calculus along with numerical simulations are used for their analysis. A power balance equation obeying a fluctuation-dissipation theorem is given. At steady state, the power injected in the harvester by random vibrations is partially dissipated by internal friction, and partially transferred to an electrical load. It is also shown that all these quantities can be calculated by solving a Lyapunov matrix equation. An algorithm based on the steepest ascent method is used to optimize the harvester. Because an analytic formula for the harvested power is not available, the derivatives for the gradient estimation are calculated numerically. The algorithm converges fast, and is very efficient, giving a significant advantage in optimization problems where a large parameter space must be explored. Finally, it is shown that the networked structure harvests significantly more power with respect to a single-degree-of-freedom system.