Dynamic stability of a moving column subject to axial acceleration and force perturbations

The equation of motion of a free‐free moving column with a prescribed axial acceleration is formulated based on Hamilton’s principle and the assumed mode method. The slender column is used as a simple model for a missile or a launched vehicle. The column is under the action of aerodynamic forces which are modelled as axial external loads at the ends of the column. The effects of axial sinusoidal perturbations in respect of axial acceleration and the external loads are then examined using Bolotin’s method. The respective regions of instability are determined by converting the resulting equations of boundary frequencies to the standard form of a generalized eigenvalue problem. Instability regions for various combinations of external loads and axial acceleration of the column are presented.