Divergence instabilities of nonuniformly prestressed travelling webs

Abstract

The phenomenon of edge-buckling in an axially moving stretched thin elastic web is described as a nonstandard singularly perturbed bifurcation problem, which is then explored through the application of matched asymptotic techniques. Previous numerical work recently reported in the literature is reevaluated in this context by approaching it through the lens of asymptotic simplifications. This allows us to identify two distinct regimes characterised by qualitative differences in the corresponding eigendeformations; some simple approximate formulae for the critical eigenvalues are also proposed. The obtained analytical results capture the intricate relationship between the critical speeds, the background tension, and other relevant physical and geometric parameters that feature in the mathematical model.