OPTIMUM SHAPE DESIGN AGAINST FLUTTER OF A CANTILEVERED COLUMN WITH AN END-MASS OF FINITE SIZE SUBJECTED TO A NON-CONSERVATIVE LOAD

Abstract

Optimum design for dynamic stability of slender cantilevered columns subjected to a follower force, due to a rocket thrust, is investigated. The aim is to determine the tapering of the column which maximizes the critical value of the rocket thrust (at which flutter is initiated) under the constraint of constant length and volume of the column. The rocket thrust is assumed to be produced by a solid rocket motor mounted at the tip end of the column. The rocket motor is simplified as a massive ball with the same material density as the column. Based on experimental evidence [1, 2] it is argued that a mathematical model without damping gives the practical stability limit if internal and external damping is small and the rocket thrust acts only in a short interval of time. Optimum columns are determined for various sizes of the end-ball (rocket motor). For small sizes, the critical thrust can be significantly increased by optimization, about eight times. By practical (experimental realizable) values of the mass ratio μ=(mass of end-ball)/(mass of column) the critical thrust can only be increased 1·3–1·4 times which is similar to the case of a pure conservative (dead) end load. Also, it is found that the great sensitivity to small changes in design parameters, which significantly complicates optimization of the pure Beck's column, is not present for practical values of μ. It is argued then, that the ‘pure’ Beck's column should be considered as a theoretical limit case of vanishing end-mass.