Wrinkling of a normally loaded, spinning, elastic membrane: An asymptotic approximation

Abstract

This paper revisits recent work on the edge wrinkling experienced by spinning circular membranes loaded by a transverse uniform pressure. The corresponding stability analysis is carried out within the framework of the Föppl–von Kármán nonlinear plate theory. It is shown herein that the effect of rotation of the membrane is similar to an in-plane tension applied on its outer perimeter, an observation that proves to be quite effective in obtaining a tight upper bound for the critical wrinkling load of the problem. Comparisons between the simplified model and direct numerical simulations of the full eigenproblem provide further insight into the accuracy and limitations of the derived results.