Stability Analysis of Tapered Beck's Columns with a Tip Mass and an Elastic Spring at Free End

The purpose of this paper is to investigate the stability of tapered Beck's columns carrying a tip mass of rotatory inertia with translational elastic support at the free end. The linearly tapered solid rectangular cross-section is adopted as the column taper. The differential equation governing free vibrations of such Beck's columns is derived using the Bernoulli-Euler beam theory. Both the divergence and flutter critical loads are calculated from the load-frequency curves which are obtained by solving the differential equation. The critical loads are presented as functions of various nondimensional system parameters: the taper type, the subtangential parameter, mass ratio and spring stiffness.