Flutter of spring-mounted flexible plates in uniform flow

Abstract

A fluid-structure interaction (FSI) system is studied wherein a cantilevered flexible plate aligned with a uniform flow has its upstream end attached to a spring mounting. This allows the entire system to oscillate in a direction perpendicular to that of the flow as a result of the mounting's dynamic interaction with the flow-induced oscillations, or flutter, of the flexible plate. We also study a hinged-free rotational-spring attachment as a comparison for the heaving system. This variation on classical plate flutter is motivated by its potential as an energy-harvesting system in which the reciprocating motion of the support system would be tapped for energy production. We formulate and deploy a hybrid of theoretical and computational modelling for the two systems and comprehensively map out their linear-stability characteristics at low mass ratio. Relative to a fixed cantilever, the introduction of the dynamic support in both systems yields lower flutter-onset flow speeds; this is desirable for energy-harvesting applications. We further study the effect of adding an inlet surface upstream of the mount as a means of changing the destabilising mechanism from single-mode flutter to modal-coalescence flutter which is a more powerful instability more suited to energy harvesting. This strategy is seen to be effective in the heaving system.However, divergence occurs in the rotational system for low spring natural frequencies and this would lead to its failure for energy production. Finally, we determine the power-output characteristics for both systems by introducing dashpot damping at the mount. The introduction of damping increases the critical speeds and its variation permits optimal values to be found that maximise the power output for each system. The addition of an inlet surface is then shown to increase significantly the power output of the heaving system whereas this design strategy is not equally beneficial for the rotational system.