Parametric studies of the dynamic evolution through a fold

A brief study is presented of the dynamic behaviour of a system approaching a fold (also known in the literature as a limit point or saddle-node bifurcation). A study of the transient dynamics shows that it is possible to predict the incipient loss of stability of equilibrium by using an appropriate frequency relationship. The relative advantages of an ω2 and an ω4 predictor, respectively, are fully explored for damped and undamped systems. Digital computations are used to explore the range of validity of the predictions and a simple laboratory study of the snap-through buckling of an elastic cantilevered column provides an experimental verification. © 1986 Academic Press Inc. (London) Limited.