Stability and scalability of piezoelectric flags

TL;DR

This paper models the impact of piezoelectric materials on the flutter dynamics and energy harvesting efficiency of flexible flags in fluids, revealing optimal circuit configurations and material choices for different fluid environments.

Contribution

It develops a coupled fluid-solid-electric model for piezoelectric flags and analyzes the effects of circuit tuning and material properties on flutter and energy harvesting performance.

Findings

Resistive circuits increase flutter speed and power with higher electro-mechanical coupling.

Optimal resistance maximizes flutter speed and energy harvesting.

RL circuits tuned to vibration frequency enhance power and reduce flutter speed in heavier fluids.

Abstract

We investigate the effect of piezoelectric (PZT) material on the flutter speed, vibration mode and frequency, and energy harvesting power and efficiency of a flexible flag in various fluids. We develop a fully coupled fluid-solid-electric model by combining the inviscid vortex sheet model with a linear electro-mechanical coupling model. A resistance only circuit and a resonant resistance-inductance (RL) circuit are considered. For a purely resistive circuit, an increased electro-mechanical coupling factor results in an increased flutter speed, vibration frequency, averaged electric power and efficiency. A consistent optimal resistance is found that maximizes the flutter speed and the energy harvesting power. For a resonant RL circuit, by tuning the inductance to match the circuit frequency to the flag's vibration frequency, the flutter speed can be greatly decreased, and a larger averaged power and efficiency are obtained. We also consider a model scale set-up with several commonly used commercial materials for operating in air and water. Typical ranges of dimensionless parameters are obtained for four types of material that span a wide range of solid density and rigidity values. We find that the resistance only circuit is more effective when the flag is placed in a lighter fluid (e.g. air), while the RL circuit is able to reduce the flutter speed when the flag is placed in a heavier fluid (e.g. water).