Optimal placement and tuning of multiple tuned mass dampers for suppressing multi-mode structural response

Abstract

The optimal design of multiple tuned mass dampers (multiple TMD\'s) to suppress multi-mode structural response of beams and floor structures was investigated. A new method using a numerical optimizer, which can effectively handle a large number of design variables, was employed to search for both optimal placement and tuning of TMD\'s for these structures under wide-band loading. The first design problem considered was vibration control of a simple beam using 10 TMD\'s. The results confirmed that for structures with widely-spaced natural frequencies, multiple TMD\'s can be adequately designed by treating each structural vibration mode as an equivalent SDOF system. Next, the control of a beam structure with two closely-spaced natural frequencies was investigated. The results showed that the most effective multiple TMD\'s have their natural frequencies distributed over a range covering the two controlled structural frequencies and have low damping ratios. Moreover, a single TMD can also be made effective in controlling two modes with closely spaced frequencies by a newly identified control mechanism, but the effectiveness can be greatly impaired when the loading position changes. Finally, a realistic problem of a large floor structure with 5 closely spaced frequencies was presented. The acceleration responses at 5 positions on the floor excited by 3 wide-band forces were simultaneously suppressed using 10 TMD\'s. The obtained multiple TMD\'s were shown to be very effective and robust.