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Leveraging smooth nonlinearities in vibration energy harvesters has been shown to improve the potential for kinetic energy capture from the environment as a transduced, alternating flow of electrical current. While researchers have closely examined the direct current power delivery performance of linear energy harvesters, there is a clear need to quantify the direct current power provided by nonlinear harvester platforms, in particular those platforms having bistable nonlinearities that are shown to have advantages over other smooth nonlinearities. In addition, because real world excitations are neither purely harmonic nor purely stochastic, the influences of an arbitrary combination of such excitation mechanisms on power delivery must be uncovered. To bring needed light to these roles and opportunities for nonlinear energy harvesters to provide direct current electrical power for numerous applications, this research formulates a new analytical approach to characterize simultaneous harmonic and stochastic mechanical and electrical responses of nonlinear harvester platforms subjected to realistic base excitation. Based on the outcomes of analytical, numerical, and experimental studies, it is found that additive stochastic excitation may result in direct current power enhancement via perturbation from a low amplitude state particularly at low frequencies or reduce the direct current power by preventing persistent snap-through response often at higher frequencies. When the noise standard deviation is greater than the harmonic amplitude by approximately two times, the advantages to direct current power generation are more often realized.

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