Post-critical behavior of Beck's column with a tip mass

This study examines how a tip mass with rotary inertia affects the stabilit y of a follower-loaded cantilevered column. Using nonlinear modeling and pe rturbation analysis, expressions are set up for determining the stability o f the straight column and the amplitude of post-critical flutter oscillatio ns. Bifurcation diagrams are given, showing how the vibration amplitude cha nges with follower load and other parameters, These results agree closely w ith numerical simulation. It is found that sufficiently large values of tip mass rotary inertia can change the primary bifurcation from supercritical into subcritical. This can imply very large motions for follower loads just beyond critical, contrasting the finite amplitude motions accompanying sup ercritical bifurcations. Also, the straight column may be destabilized by a sufficiently strong disturbance at loads far below the value of critical l oad predicted by linear theory. A similar change in bifurcation is found to occur with increased external (as compared to internal) damping, and with a shortening in column length. These effects are not revealed by linear mod eling and analysis, which may consequently fail to predict even qualitative ly the real critical load for a column with tip mass. (C) 2001 Elsevier Sci ence Ltd. All rights reserved.