Exact dynamic stiffness for axial-torsional buckling of structural frames

A dynamic axial-torsion buckling theory is proposed for analysis in structural mechanics. Second order effects of the axial force and torque are considered. The consistent natural boundary moments and forces are given to ensure the symmetry of the dynamic stiffness matrix in fulfilling the requirement of the reciprocal theorem. The exact dynamic stiffness matrix is obtained for the first time using power series expansion. Generally distributed axial force can be analyzed without difficulty. It is pointed out that non-uniform sections may not be effectively analyzed due to the convergent problem. The interaction diagrams due to vibration frequency, axial force and torque are studied in details.