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

Abstract

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 mounting’s dynamic interaction 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 very robust to spatial and temporal discretisation. 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.