Dynamics of a Tube Conveying Fluid

TL;DR

This paper develops a nonlinear evolution equation to analyze the dynamic behavior of a fluid-conveying tube with different boundary conditions, revealing flutter and rotation instabilities through stability analysis and numerical simulations.

Contribution

It introduces a new nonlinear model for fluid-conveying tubes and compares stability under different boundary conditions, highlighting distinct instability mechanisms.

Findings

Clamped boundary conditions lead to flutter instability.

Hinged boundary conditions lead to rotation instability.

Numerical simulations confirm nonlinear behaviors and stability analysis results.

Abstract

A tube conveying a large amount of fluid with a free outlet does not sit still. We construct and analyze a nonlinear evolution equation describing such phenomena. Two types of boundary conditions at the inlet are considered, one for which it is clamped and one for which it is hinged. Analyzing the linear stability of the trivial solution, we find that with the former boundary conditions, it exhibits a ``flutter'' instability, while with the latter boundary conditions, it exhibits a ``rotation'' instability. These instabilities and the nonlinear behaviors of the system are also studied numerically.