Dynamic stability of thin-walled column under periodic excitation

摘要

The dynamic stability of variable stiffness thin-walled column subjected to periodically alternating axial force is analysed in this paper. Here, the variable stiffness means that it changes with periodically alternating axial force as for non-linear geometry stiffness matrix of thin-walled column. Damping is not considered at present. A system of second-order differential equations with period coefficients of the Mathieu type describes the dynamic stability of thin-walled columns without damping. To solve the problem the finite element method is applied which can greatly reduce the process of simplification. By using MATLAB package, a computer program is developed to calculate the region of dynamic instability without damping corresponding to bending vibration, torsion and warping coupling vibration. The results prove to be more efficient and credible, compared with other calculation methods.