In this work, the response of a single degree of freedom electromagnetic energy harvester to a white noise base excitation is analysed using the Fokker-Planck-Kolmogorov equation. In this case, a magnetic levitation device with Duffing-type nonlinearities is investigated. It is shown analytically that the introduction of the nonlinearity has the effect of reducing the maximum displacement amplitude of the device centre magnet while having no effect on its expected relative velocity. As a result, it is concluded that the nonlinearity can be used to aid the construction of smaller devices without effecting their power output. The feasibility of applying this idea to real devices is then investigated experimentally. Subsequently, the response of the device when connected to a load resistance is analysed. It is shown that, when under a white noise base excitation, the principle of impedance matching does not always appear to lead to the maximum transfer of energy through the load resistor.
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