Piezoelectric vortex induced vibration energy harvesting in a random flow field - Sondipon Adhikari (Smart Materials and Structures, 2020)
Vibration-based energy harvesters have significant potential for sustainable energy generation from ambience for micro-scale systems like wireless sensor networks and similar low power electronic devices. Vortex-induced vibration (VIV) is one of the richest sources for such power generation for devices installed within a fluid environment. However, uncertainty in the direction and magnitude of the free stream velocity could affect the performance of such systems. We have first developed the mathematical model of a piezoelectric cantilever beam with end mass vibrating under the influence of VIV. The piezo patch is assumed to be in the unimorph and bimorph configurations. From the unimodal dynamic response of the system, an equivalent single degree of freedom mechanical model is developed. This is further integrated with the electrical model of the piezoelectric system without and with an inductor. The energy harvested from the deterministic harmonic excitation is estimated against the non-dimensional velocity parameter. A random process model is developed considering the excitation force due to vortex shedding to be a bounded, weakly stationary and narrowband random process. The power spectral density of the random process is obtained using the Fourier transform of the auto-correlation function. The dynamic response of the energy harvester is obtained against such random excitations. The expressions of the mean power are obtained in closed-form corresponding to the cases without and with the inductor integrated to the electrical circuit. It is observed that while for cases without the inductor, the average harvested power monotonically decreases with increase in damping ratio and decrease in the coupling factor; for models with the inductor, an optimal inductor constant exists corresponding to the maximum mean-power condition. The extensive analytical modelling and initial representative results are expected to pave the way for the practical design of VIV based piezoelectric energy harvesting system subjected to stochastic excitation.