A Unified Approach to Galloping of Rectangular Cylinders with or Without a Stationary Splitter Plate

Abstract

Galloping is a single-degree-of-freedom flutter of a bluff body in translation in a cross-flow direction. Despite the great success of the quasi-steady theory [1], two important problems related to high-speed galloping remain unsolved. The first one concerns the effects of decreasing reduced velocity on galloping. Obviously, the quasi-steady galloping theory is only valid in the high-speed range for which Ū >> Ūr. Here, Ū and Ūr are defined respectively as Ū=U/fh and Ūr=U/fvh, where U is the flow velocity, h is the length scale of a bluff body, f is the body frequency, and fv is the frequency of vortex shedding for the body at rest under the same flow conditions. The effects of two flow modules, i.e., wake undulation and vortex resonance, are both neglected in the quasi-steady galloping theory. Wake undulation becomes increasingly more influential on galloping as Ū is lowered, and furthermore, as Ūr, the vortex-resonance velocity is approached, strong interaction between galloping and vortex excitation can take place.