Isolated large amplitude periodic motions of towed rigid wheels

TL;DR

This paper analyzes a mechanical model of towed wheels exhibiting large amplitude periodic motions, identifying bifurcations and isolated oscillation regions that are critical for safe engineering design.

Contribution

It applies bifurcation theory and numerical continuation to reveal isolated large amplitude oscillations in a towed wheel model, highlighting potential engineering risks.

Findings

Identification of stable and unstable periodic motions

Detection of isola regions with large amplitude oscillations

Implications for avoiding dangerous vibrations in design

Abstract

This study investigates a low degree-of-freedom (DoF) mechanical model of shimmying wheels. The model is studied using bifurcation theory and numerical continuation. Self-excited vibrations, that is, stable and unstable periodic motions of the wheel, are detected with the help of Hopf bifurcation calculations. These oscillations are then followed over a large parameter range for different damping values by means of the software package AUTO97. For certain parameter regions, the branches representing large amplitude stable and unstable periodic motions become isolated following an isola birth. These regions are extremely dangerous from an engineering view-point if they are not identified and avoided at the design stage.