On the Feasibility of Using Linear Fluid Dynamics in an Overall Nonlinear Model for the Dynamics of Cantilevered Cylinders in Axial Flow

Abstract

A curiosity-driven study is presented here which introduces and tests an analytical model to be employed for describing the dynamics of cantilevered cylinders in axial flow. This model is called “hybrid” because it encompasses linear fluid dynamics and nonlinear structural dynamics. Also, both the linear and fully nonlinear models are recalled here. For all these models Galerkin’s method is used to discretize the nondimensional equation of motion. For the hybrid and nonlinear models a numerical method based on Houbolt’s Finite Difference Method (FDM) is used to solve the discretized equations, as well as AUTO, which is a software used to solve continuation and bifurcation problems for differential equations. The capability of the hybrid model to predict the dynamical behaviour of cantilevered cylinders in axial flow is assessed by examining three different sets of parameters. Here, the main focus is put on the onset of instabilities and the amplitude of the predicted motion. According to the results given in the form of bifurcation diagrams and several tabulated numerical values, the hybrid model is proved to be unacceptable although it can predict the onset of first instability, and even the onset of post-divergence instability in some cases.