Nonconservative dynamic axial–torsional buckling of structural frames using power series

Abstract

Axial deformation is not involved in the formulation of linear buckling caused by axial force. Likewise, twisting is not present in linear buckling caused by axial torque. The dynamic axial–torsional buckling of structural frames in the presence of follower axial force will be solved by means of dynamic stiffness using power series. Variationally consistent natural boundary conditions are given so that the resulting dynamic stiffness is symmetrical for conservative loading. Some parts of the boundary forces disappeared for follower axial forces due to consistent tangency to the neutral axis. The deficiency of the power series method to deal with non-uniform sections is highlighted. New instability phenomena for a simple column are studied in detail. It is shown that columns can buckle under direct follower tension. Follower tension decreases the natural frequency initially and then increases it rapidly after a turning point. The first pair of modes about the major axis and that about the minor axis of a rectangular section column meet at one crossing point. A very small axial torque will change the crossing into flutter-like tongues. These tongues are common in compressive follower force. These tongues caused by axial torque are reported here for the first time.