Applied Mathematics Seminar

It is well known that if a column exceeds a certain critical length it will, when placed upright, buckle under its own weight. In a recent experiment Acheson and Mullin (1998) have demonstrated that a column that is longer than its critical length can be stabilized by subjecting its bottom support point to a vertical oscillation of appropriate amplitude and frequency. In this talk I shall derive the nonlinear equations that govern the stability of such a column. I will then discuss a weakly nonlinear asymptotic analysis of these equations for a column that is slightly longer than its critical length. It will be shown that such a `slightly too long column' can be stabilized by oscillating its support point, but that it may be difficult to obtain a sharp experimental determination of the stability boundary.