Effect of intermediate support on critical stability of a cantilever with non-conservative loading: Some new results

Abstract

The introduction of intermediate support can significantly alter the stability characteristics of an elastic structure subjected to non-conservative loading; this follows from investigations carried out almost three decades ago. A majority of these investigations however assume the non-conservative loading to have the form of a follower force. A new type of non-conservative loading in the from of a dynamic moment was recently introduced in the literature using both theory and experiments and it behooves us to investigate the effect of intermediate support on structures with such type of loading. The dynamic moment is proportional to the curvature of a point on the structure; critical stability is therefore investigated in the two-parameter space defined by the locations of the intermediate support and the point of curvature measurement. For a cantilever beam with terminal dynamic moment, the investigations reveal a rich set of instability transitions not observed heretofore; these include multiple stability transitions between divergence and flutter and between different modes of flutter, transitions occurring with and without jumps in the critical load, orderly and random flutter-to-flutter transitions, and multiple instability transitions involving jumps in the critical load. The jump in the critical load is also observed for the cantilever beam with follower force; this jump, which was reported to be absent in earlier work, results from the veering phenomenon.