Estimating double tuned mass dampers for structures under ground acceleration using a novel optimum criterion

Abstract

The double tuned mass dampers (DTMD), consisting of one larger mass block (i.e. one larger tuned mass damper (TMD)) and one smaller mass block (i.e. one smaller TMD), have been proposed to seek for the mass dampers with high effectiveness and robustness for the reduction of the undesirable vibrations of structures under the ground acceleration. The structure is represented by the mode-generalized system corresponding to the specific vibration mode that needs to be controlled. In light of the developed dynamic magnification factors (DMF) of the DTMD structure system, the criterion used for assessing the optimum parameters and effectiveness of the DTMD is selected as the minimization of the minimum values of the maximum DMF of the structure with the DTMD. With resorting to the maximum DMF of both the larger and smaller TMDs in the DTMD, the stroke of the DTMD is simultaneously investigated too. It is highlighted that a novel optimum objective function has been proposed in order to acquire high robust control system. Consequently, the two types of optimum goal functions (including the optimum goal function commonly used) have been applied for the optimum searching of the DTMD. The numerical results indicate that the DTMD designed in terms of the second type of optimum objective functions (i.e. the novel optimum objective function) practically provides the same effectiveness and robustness to the changes in the drift frequency ratio (DFR) as the multiple tuned mass dampers (MTMD) with the distributed natural frequencies with the total number of the TMD units equal to five and with equal total mass ratio. Likewise, the DTMD designed with resort to the second type of optimum objective functions can practically attain the same effectiveness as the TMD with equal total mass ratio. More importantly, in the robustness to the changes in the DFR, the DTMD is significantly better than the TMD, whereas in the robustness to the natural frequency tuning (NFT), measured by the frequency band width coefficient (FBWC), the DTMD is significantly better than the MTMD, thus manifesting that the DTMD is an advanced control device.