Nonlinear dynamics of a slender flexible cylinder subjected to axial flow.

摘要

This thesis deals with the nonlinear dynamics of a vertical slender flexible cylinder supported at both ends and subjected to axial flow. The goal is to study the dynamical behaviour of this system from a nonlinear point of view, both theoretically and experimentally.;Houbolt's finite difference method and AUTO are used as two numerical methods to solve the resulting set of ordinary differential equations. The centre manifold reduction method is also used as an analytical method to study the behaviour of the system in the vicinity of the pitchfork bifurcation point.;The results for a cylinder with various boundary conditions are presented in the form of bifurcation diagrams with flow velocity as the independent variable, supported by time histories, phase-plane plots, PSD plots and Poincaré maps. The influence of different parameters on the behaviour of the system is also investigated.;Three series of experiments were conducted on vertical clamped-clamped cylinders. In the first series of experiments, the downstream end of the clamped-clamped cylinder was free to slide axially, while in the second series of experiments, the downstream end was fixed. The influence of externally applied axial compression has also been studied in the second series of experiments. In the third series of experiments, a more flexible cylinder was used, and the effect of externally applied axial compression on the dynamic instability of the cylinder was also studied.;A weakly nonlinear model is derived assuming that the cylinder centreline is extensible. Nonlinear Euler-Bernoulli beam theory is used for the structure and, the fluid forces acting on the cylinder are assumed to be inviscid, frictional and hydrostatic ones. The derivation of the equations of motion is carried out in a Lagrangian framework, and the resultant equations are correct to third order of magnitude. These nonlinear partial differential equations are then recast in nondimensional form and discretized by using Galerkin's technique, giving a set of nonlinear second-order ordinary differential equations.