Simplified model for vorticity-induced vibration of a flat cantilevered plate

In this work, simplified representations of numerical models for the vorticity-induced vibration of a flat cantilevered plate are presented. A fully coupled transient finite element analysis and computational fluid dynamics simulation procedure is initially implemented. As the stiffness of the plate is varied, two fundamentally different states of vorticity-induced vibration are observed. For cases where the vortex shedding frequency of the fluid is close to the structural resonances, large structural vibrations are observed. In contrast, minimal structural deformation occurs for cases where the vortex shedding frequencies are far from the system resonances. It is shown that in the latter case, the fully coupled fluid-structure analysis can be replaced with a simplified uncoupled analysis. The fluid pressure time history obtained from solving the fluid flow over a rigid plate is used as a forcing function for the flexible plate without considering the flow field. In addition, it is shown that for a system in resonance with significant interaction of structural deflection and vortex shedding, the flowinduced forces on the structure and the structural deflections are nearly in phase. Thus, the effect of fluid on the structure is approximated to a spring. The simplified models developed in this work yield a significant reduction in the computational cost compared to the fully coupled numerical model, as well as yields a better understanding of the physical mechanisms associated with vorticity-induced vibration of a plate.