  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.
Subsequently, we study the robustness of this optimal performance to small
perturbations of the input spectrum and illustrate the advantages of nonlinear
designs relative to linear ones.
