Dynamic stiffness analysis for axial-lateral-torsional vibration

Abstract

The dynamic stiffness method enables one to model an infinite number of natural modes by means of a finite number of degrees of freedom. The method is extended to analyse the lateral-torsional vibrations of thin-wall columns under the influence of the constant axial force. The constant in-plane moment weakens the flexural mode so that at certain critical applied moments, the flexural mode buckles as the fundamental flexural frequency reaches zero. However, the constant in-plane moment hardens the torsional mode so that the torsional mode never buckles. When both torsion and flexure are considered, the interaction of the convexity of flexural characteristic curves and the concavity torsional characteristic curves becomes very complex. Since the dynamic stiffness is exact in the classical sense, the interaction can be studied easily. Numerical examples are given to show the complexity of the characteristic diagrams.