The effect of axial extension on the fluidelastic vibration of an array of cylinders in cross-flow

In this paper an improved model is developed aimed at analyzing the fluidelastic vibration of a single flexible cylinder surrounded by rigid cylinders and subject to cross-flow. Compared with other dynamical models reported previously, the nonlinearity associated with the mean axial extension of the cylinder has been accounted for in the current work. Calculations are performed to explore the effect on the nonlinear dynamics of the nonlinearity presented in the equation of motion. Numerical results show that, with increasing flow velocity just beyond a critical value, a post-Hopf limit-cycle motion occurs. For a system without loose supports, the vibration amplitude of the limit-cycle motion can be predicted by using the presented model. To understand the nonlinear dynamics of the cylinder better, a modified system with loose supports is also investigated. The impacting force induced by the loose supports was modelled by a cubic spring or by a trilinear spring. It is found, by using the theoretical model developed here, that the post-Hopf dynamics predicted with the cubic-spring representation is quite different from those predicted with the trilinear-spring representation. However, it is shown that the effect of the nonlinearity associated with the mean axial extension on the nonlinear dynamics of cylinder with loose supports is not pronounced.