Stability of a Spring-Mounted Cantilevered Flexible Plate in a Uniform Flow

A new system in fluid-structure interaction (FSI) is studied wherein a cantilevered thin flexible plate is aligned with a uniform flow with the upstream end of the plate attached to a spring-mass system. This allows the entire system to oscillate in a direction perpendicular to that of the flow as a result of the dynamic interaction of the mounting with the flow-induced oscillations, or flutter, of the flexible plate. While a fundamental problem in FSI, the study of this variation on classical plate flutter is also motivated by its potential as an energy-harvesting system in which the reciprocating motion of the support system would be tapped for energy production. In this paper, we formulate and deploy a hybrid of theoretical and computational models for the fluid-structure system and map out its linear stability characteristics. The computational model detailed is a novel fully implicit solution that is robust to spatial and temporal discretization. Compared to a fixed cantilever, the introduction of the dynamic support system is shown to yield lower flutter-onset flow speeds and a reduction of the order of the mode that yields the critical flow speed; these effects would be desirable for energy-harvesting applications