Dynamics of an articulated cylinder in annular flow via non-linear and partially linearized versions of an analytical model

This paper deals with the non-linear dynamics of an articulated system of two rigid cylinders interconnected by rotational springs, within a pipe conveying fluid, with fluid flowing downward in the relatively narrow annular space. The impacting of the articulated cylinder system on the external pipe is modelled by a cubic spring. The behaviour of the articulated cylinder system is studied for flow velocities higher than the critical value at which a flutter or a divergence instability occurs. Two models are constructed for this system, depending on the form of equations of motion considered: in the first model, the dynamics of the system when no impact occurs with the outer pipe is described by a set of non-linear equations in which the non-linearities are taken into account approximately to order three via Taylor expansions of the trigonometric functions of state variables; in the second case, these equations are linearized. For both models, the dynamical behaviour of the system is illustrated by phase plane portraits, bifurcation diagrams, power spectra and Poincare sections. The results obtained via these two models are compared qualitatively and quantitatively. (C) 1996 Academic Press Limited