Report No. 496, general theory of aerodynamic instability and the mechanism of flutter

In this paper, we study the problem of harmonic oscillations of a flanged lamina in a quiescent Newtonian incompressible viscous fluid. We conduct a comprehensive fluid–structure interaction investigation with the goal of assessing the effect of the presence of the flanges on the added mass and hydrodynamic damping experienced by the oscillating solid. We determine the complex nonlinear hydrodynamic function incorporating these effects via its real and imaginary parts, respectively, and its dependence on three nondimensional parameters that govern the flow evolution. We further investigate in detail the flow physics and the effects of nonlinearities on vortex shedding, convection, and diffusion in the vicinity of the oscillating structure. We find that the added mass effect is relatively independent of the oscillation amplitude and increases with the flange size. On the other hand, the hydrodynamic damping effect is remarkably affected by the interplay of geometry and dynamic parameters resulting into a peculiar non-monotonic behavior. We show the existence of a minimum in the hydrodynamic damping which can be attained via specific control of vortex–structure interaction dynamics and discuss its properties and significance from a physical perspective through analysis of the relevant flow fields. This novel finding has potential application for damping reduction in elastic systems where reduction of energy losses and increase of oscillation quality factor are desired.