A comparative performance analysis of electrically optimized nonlinear energy harvesters

Depending on the shape of their potential energy function, nonlinear vibratory energy harvesters (VEHs) can be classified either as mono- or bi-stable. The complex dynamic responses of such harvesters make it difficult to accurately analyze their performance relative to one another. In this paper, we aim to tackle this issue by comparing the performance of these two classes in response to harmonic fixed-frequency excitations under optimal electric loading conditions. To achieve this goal, the mathematical model of a generic nonlinear VEH capable of operating in both of the mono- and bi-stable configurations is considered. Using perturbation methods, analytical expressions for the steady-state output power are obtained. The output power is then optimized with respect to the time constant ratio which represents a direct measure of the electric load. We study the variation of the optimal output power with the excitation frequency in both configurations for different potential shapes and excitation levels. It is shown that, tuning the optimal time constant ratio close to the excitation frequency results in maximum power transduction in both configurations. Results also illustrate that bi-stable VEHs produce higher power levels than mono-stable ones under optimal electric loading conditions regardless of the shape of the potential function.