Limits on the power available to harvest from broadband random excitation

With the large diversity in energy harvesters aiming to extract maximum power from broadband excitations, it is important to know what the maximum power achievable is. This paper derives new upper bounds on the available power for a harvester with general nonlinear stiffness coupled to a nonlinear electrical circuit. White noise base excitations are known to input power proportional to the total oscillating mass of the system and the magnitude of the spectral density of the noise regardless of the details of the oscillating system. This power is split between undesirable mechanical damping and useful electrical dissipation with the form of the stiffness profile and device parameters determining the relative proportions in each dissipation mechanism. An upper bound on electrical power is sought and, provided certain conditions are met, shown to be a simple function of relatively few system parameters and, importantly, independent of the stiffness profile or electrical nonlinearity. The benefits of knowing the upper limits on power are threefold: to guide optimal harvester design, to assess how close to optimal current devices are and to provide a preliminary estimation of the harvester mass necessary in a given operating environment for a given power requirement