Vibration energy harvesting paradigms that seek to exploit the unique characteristics of nonlinear and stochastic systems are currently emerging as an important aspect of frontier research in energy sustainability. In particular, the ubiquitous nature of ambient mechanical vibrations and recent results obtained in the dynamics of micro and nano scale oscillatory systems together suggest the potential efficacy of vibration energy harvesting for the powering of small scale electronic mobile devices. In this context, the inherent advantages of using nonlinear systems over linear ones for energy harvesting are currently well established. In addition, the inherently random nature of ambient vibrations as well as the emergence of phenomena such as stochastic resonance indicates the imperativeness of a stochastic approach. Computational and experimental studies of energy harvesting involving individual nonlinear oscillators that take into account some of the above mentioned features have recently been reported in the literature. In this article, the authors present a new approach to the problem by introducing an analytical framework based on the Fokker-Planck formalism. In particular, the framework is applied to a nonlinearly coupled array of micro-scale oscillators in order to investigate the potential advantages of stochastic effects in coupled arrays for energy harvesting. The influence of varying coupling strengths as well as noise intensity on harvestable energy is studied for the case of a nonlinearly coupled micro-cantilever array. It is noted that the micro-scale arrays of the type under consideration have already been employed in experimental investigations of energy localization effects and hence are currently available for technological applications. In conclusion, the analytical framework introduced and the results obtained in this article are expected to contribute to a fundamental understanding of how the synergistic effects of nonlinear and stochastic phenomena could contribute to the development of novel methods for efficient vibration energy harvesting.

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