Model reduction in stochastic vibration energy harvesting using compressive sampling

Vibration energy harvesters are designed to gather parasitic energy from the motion of their host structures. In many germane scenarios, this motion is broadband; however, the preponderance of design criteria appearing in the literature for vibration energy harvesters considers sinusoidal base excitation at a single frequency. While this analysis often leads to analytical formulas for estimating power harvested, they fail to account for the contribution of multiple frequency components of the host motion and the excitation of higher vibration modes of the transducer. In this paper, an attempt is made to provide brief, analytical approximation of these additional factors. To wit, the single-mode, single-frequency power formula is extended to multi-frequency inputs and multiple modal excitations by matching each base acceleration frequency component to at most one mode of vibration whose half-power bandwidth that frequency falls within. Then, due to orthogonality, the expected power can be written as the sum of the contributions of the individual frequency components. To demonstrate the accuracy of this approximation, recorded acceleration signals from a car idling and a person walking are used as inputs, and predictions from the approximation are compared to results from full simulations. Approximations using only three frequency components are shown to be more than 80% accurate, with increased accuracy as the base acceleration signal becomes narrower in bandwidth. The effects of charge cancellation in the higher modes are also considered using simulations and the aforementioned approximations. These studies show that rectifying the strain in the higher modes is only beneficial if these modes contribute significantly to the power harvested. The approximate formulas derived in this paper are useful for making this determination. (Some figures may appear in colour only in the online journal)