Judging Criterion of Controlled Structures with Closely Spaced Natural Frequencies

The structures with closely spaced natural frequencies widely exist in civil engineering; however, the judging criterion of the density of closely spaced frequencies is in dispute. This paper suggests a judging criterion for structures with closely spaced natural frequencies based on the analysis on a controlled 2-DOF structure. The analysis results indicate that the optimal control gain of the structure with velocity feedback is dependent on the frequency density parameter of structure and the maximum attainable additional modal damping ratio is 1.72 times of the frequency density parameter when state feedback is applied. Based on a brief review on the previous researches, a judging criterion related the minimum frequency density parameter and the required mode damping ratio was proposed.