Abstract:

Structures with closely spaced natural frequencies exist widely, while the judging criterion of the density of closely spaced frequencies is in dispute. A judging criterion for structures with closely spaced natural frequencies based on the analysis on a controlled two degree of freedom structure was suggested. [JP2]The perturbation method was applied in the analysis and the results were verified by numerical simulations. It was shown that the optimal control gain of the two degree of freedom structure with velocity feedback was dependent on the frequency density of the structure, which was  quantatively equal to the maximum additional mode damping ratio of the structural mode with higher frequency. When usingstate feedback, the maximum attainable additional mode damping ratio is 3 times the frequency density parameter. The results indicated that the frequencies density parameter was closely related to the optimal modal damping ratio of the structure. Based on a brief review of previous research, a judging criterion related the minimum frequency density parameter and the required modedamping ratio were proposed, which has a clear physical meaning.

Key words: controlled structure; closely spaced natural frequencies; judging criterion; perturbation method