Divergence and flutter instabilities of a cantilever beam subjected to a terminal dynamic moment

The effects of a dynamic terminal moment on the stability characteristics of a cantilever beam, not studied heretofore, are investigated using both theory and experiments. The terminal moment is assumed to be proportional to the slope or curvature of the beam measured at some point along its length. The moment is non-conservative when it is curvature-dependent as well as when it is slope-dependent provided the measurement is not taken from the free end of the beam. Irrespective of whether the moment is slope-dependent or curvature-dependent, the beam loses stability through divergence when the constant of proportionality is positive, and through flutter when the constant of proportionality is negative. For the case where the terminal moment is proportional to the negative slope or negative curvature, multiple stability transitions can occur and higher modes of flutter instability are induced as the point of measurement shifts from the fixed end to the free end of the beam. These conclusions are drawn through analytical and numerical investigations of stability. In the experimental component of work, the terminal moment is designed to be curvature-dependent for ease of measurement. Flutter oscillations are observed at or slightly beyond the point of instability and the frequency and mode shape of the oscillations are found to match reasonably well with those predicted analytically. (C) 2019 Elsevier Ltd. All rights reserved.