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 dir
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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 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.
1 Introduction In the recent study of simply supported or cantilevered plates in uniform axial flow first studied by Kornecki et al. (1976), a popular idea has been that of using the flutter instabilities observed in the system to generate useful electrical energy harvested by various means; see for examples Allen and Smits (2001) and Tang et al. (2009). This has led us to investigate the linear stability of a new fundamental R. M. Howell (&) A. D. Lucey Fluid Dynamics Research Group, Department of Mechanical Engineering, Curtin University of Technology, GPO Box U1987 Perth WA 6845, Australia e-mail: [email protected]
Y. Zhou et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, DOI: 10.1007/978-3-642-40371-2_45, Springer-Verlag Berlin Heidelberg 2014
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Fig. 1 The fluid-structure interaction under consideration
system, where the cantilever is not fixed but can move freely in the vertical axis being attached at its leading edge to a rigid base by mounting it upon a linear spring; this new system is depicted in Fig. 1 that also shows the inclusion of a rigid-inlet surface upstream and fixed to the cantilever. A future application of this system would be an energy-harvesting device; this would be achieved through the addition of a linear damper as part of the spring-mass system as shown in Fig. 1. In this paper we combine the exploratory findings of our preliminary studies—see Howell and Lucey (2012a, b)—and present definitive key results. In the absence of damping we map out the dynamics of the parameter space that we find depends upon the mass ratio and the critical velocity and additionally the natural frequency of the support of the spring-mass system and the length and mass of the
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