Performance Barriers for Single-Degree-of-Freedom Energy Harvesters Under Generic Stochastic Excitation

We develop performance criteria for the objective comparison of different classes of single-degree-of-freedom oscillators under stochastic excitation. For each family of oscillators, these objective criteria take into account the maximum possible energy harvested for a given response level, which is a quantity that is directly connected to the size of the harvesting configuration. We prove that the derived criteria are invariant with respect to magnitude or temporal rescaling of the input spectrum and they depend only on the relative distribution of energy across different harmonics of the excitation. We then compare three different classes of linear and nonlinear oscillators and using stochastic analysis tools we illustrate that in all cases of excitation spectra (monochromatic, broadband, white-noise) the optimal performance of all designs cannot exceed the performance of the linear design.