An Investigation of Nonlinear Models for a Cylinder Row in a Cross Flow

An array of elastically supported cylinders placed in a uniform fluid flow perpendicular to their long axis has been known to perform large-amplitude oscillations when the flow velocity is increased past a critical value. Experimental investigations have shown that the linear stability of the cylinder row is lost through a subcritical Hopf bifurcation resulting in the now well-known hysteresis regime. In this study, we investigate the nonlinearities in the dynamics of the fluid-elastic system with particular emphasis on capturing the global bifurcation behavior of the cylinders by proposing two nonlinear models. Although the proposed nonlinear models are mostly arbitrary, when appropriate choices are made for the unknown coefficients in the models, based on the theory of center manifolds and normal forms, the predictions of the models are reasonable. While one of the models captures the experimental bifurcation diagram qualitatively, the other nonlinear model exhibits secondary bifurcation, resulting in coexisting periodic and quasi-periodic solutions.