In many scenarios where vibration energy harvesting can be utilized – particularly those involving bio-motions or environmental disturbances – energy sources are broadband and non-stationary.  On the other hand, design procedures have been predominantly developed for harmonic or white noise excitation, specifically for single degree of freedom approximations of the transducer.  In this study, a general approach for design optimization of cantilevered, piezoelectric energy harvesters in the presence of band-limited, white-noise excitation is outlined.  Human motions such as walking, running, and riding in a car are considered; these complex waveforms are distilled into a small set of dominant features with regard to their impact on the power output of the device.  These features are used to inform the modal truncation of the transducer model such that only the modes that contribute significantly to the energy harvested are retained.  These reduced-order models are then used in a design optimization process for each vibration energy source.

The results of this optimization indicate that it is impossible to design an efficient linear transducer for low frequency sources, such as walking, without resorting to heavy masses or large dimensions.  Therefore, a non-linearity is introduced in the form of frequency up-conversion; this technique uses a magnetic tip mass inside a ferrous enclosure to create a sequence of potential wells.  The transition of the tip mass between the wells induces a pluck followed by a free response, similar to an impact.  The dynamics of the base motion and the free response are then decoupled by (1) predicting how often the plucks occur and what their initial deflections are and (2) calculating the subsequent free response to each pluck.  Simulations show that the nonlinear response converges to the impact-based approximation at low frequencies (compared to the fundamental natural frequency), whereas it converges to the linearization of the system in the vicinity of the fundamental natural frequency.  Hence, the impact-based approach shows utility for modeling low-frequency energy harvesting using frequency up-conversion.  This is demonstrated by applying several low-frequency measured acceleration waveforms that are dominated by impacts in case studies.