Vibration of structures with variable stiffness

The general assumption is that stiffness matrix is constant in structures. But if the loads increase, deformation-load curve becomes nonlinear. The aim of this study is to analyze the vibration of a structure under these facts. The chosen sample problem is a steel single storey frame with a horizontal force. At first, classical stiffness matrix is determined under static loads. Then the structure has been reduced to a unique mass-spring system with increasing loads. It is accepted that material is ideal elasto-plastic. The change of stiffness under increasing loads will be calculated by plastic analysis. The system is not like the beginning after first plastic hinge occurs and degree of freedom of the system changes. If the load increases the decreasing of stiffness matrix continues. It is accepted that stiffness matrix is constant until first plastic hinge occurs. Also, it is accepted that the stiffness matrix is also constant between first and the second plastic hinges. By this way, a curve is obtained between load and stiffness matrix and the stiffness-force diagram has been plotted. In addition, the positions of plastic hinges have been controlled by SAP2000 computer program. Finally, the forced vibration of the sample structure under an harmonic load has been investigated. It is clear that the external load varies by time. Then the force-time diagram and the stiffness-time graphic have also been plotted under increasing loads. The damping coefficient of the system must be calculated for every stiffness value by choosing a initial value for system damping. The displacement-time curve has also been given. The operations of increasing loads have been repeated for decreasing loads. Also the displacement-time curves for increasing and decreasing loads have been combined and they have been shown on a single diagram.