Displacement Response Analysis of Multi-degree-of-Freedom System

Abstract

This research project has two challenges, both of which study the solution method of displacement response in different situations of multi-degree-of-freedom system. The first challenge focuses on the displacement response of an ideal two-story structure. At the beginning, only the stiffness coefficient was introduced into the structure, and no external forces were applied to the two-story structure. This is a system with two degrees of freedom. The motion equation can be sorted out through force analysis. After the initial conditions are given, the motion equation can be solved by using mode superposition method, and the position response of the system can be determined. In the latter part, damping and external forces applied on the structure are taken into consideration, making the problem studied in this project more like the real situation. When analyzing a real problem, it is common to assume a large number of degrees of freedom to make the result more accurate, such as 100 degrees of freedom or more. In this case, the mode superposition method is still applicable. The reasons for its application will be discussed. The second challenge mainly solves the problem of a static undamped system with impact loads. The reason for choosing no damping is that under the influence of impact load, the maximum response of the structure can be reached very quickly and it would be too late for damper to absorb energy. Then the position response of the structure under changing external force will be analyzed. At 3 different phases Duhamel integral was used and the approximate expressions will be written down.