A Comparison of Tyre Representations in a Simple Wheel Shimmy Problem

A simple system capable of wheel shimmy is analysed in three different ways and the results are compared. The tyre in each case is taken to be representable by a “taut string”, and the three ways involve (a) developing a digital tyre simulation which operates sequentially with a digital simulation of the mechanical system, (b) representing the tyre responses by linear constant coefficient differential equations derived empirically to match the string responses, and (c) as in (b) but employing fundamentally derived equations which approximate the exact string responses. The approximations are shown to give good results at reduced frequencies typical of the wheel shimmy phenomenon.