Nonlinear analysis of the flow-induced vibration of a circular cylinder with a splitter-plate attachment

Abstract

The nonlinear characteristics of the flow-induced vibration of an elastically-supported cylinder-plate assembly are investigated using numerical simulations of the flow past the assembly at a low-Reynolds number Re=100. The beating phenomenon in the time series of the transverse (lift) force coefficient for both vortex-induced vibration and galloping is studied. The dynamical characteristics of the beating are elucidated using local attributes (local frequency), global attributes (periodicity and symmetry), and the properties of the energy transfer (per unit time) between the cylinder-plate assembly and the surrounding fluid. From this analysis, five distinct types of beating for a cylinder-plate assembly are identified. The nonlinear dynamical characteristics is investigated using a number of methodologies such as the power spectral density, the phase-plane portrait and the Poincaré section. The analysis implies the existence of a close relationship between the multiple characteristic frequencies in the power spectrum and the beating observed in the time variations. Three types of nonlinear oscillations in a cylinder-plate assembly have been identified and characterized in terms of the nature of their limit cycles in the phase plane and the point set distribution in the Poincaré section. The wake mode of a cylinder-plate assembly during beating is found to be invariably asymmetric with highly irregular vortex shapes, e.g., a right-angled vortex designated as SA and a crescent-shaped vortex designated as SB—multiplets (groups) of vortices involving either SA or SB with two elliptically-shaped vortices are closely associated with the observed beating.