Abstract:  oscillations of a structure under the ground acceleration.The structure is represented by its mode-generalized system in the specific vibration mode being controlled using the mode reduced-order method.The optimum parameters of  the MTMD are investigated to reveal the influence of the important parameters on the effectiveness and robustness of the MTMD with resorting to a numerical searching technique.The parameters include the mass spacing,frequency spacing,average damping ratio,tuning frequency ratio,total mass ratio and total number.The criterion,which can be stated as the minimization of the minimum values of the maximum dynamic magnification factors (i.e.Min.Min.Max.DMF),is selected for the optimum searching.In the present paper,for the sake of comparison,the MTMD(II) with each TMD being identical stiffness and damping coefficient but unequal mass,whose natural frequencies take on a uniform distribution,is also taken into consideration.It is demonstrated that any further increase in the total number of the MTMD will not result in the near-zero damping ratio with the exception of the case of  and n=21, and the MTMD can provide higher damping with higher total mass ratio above 0.01.It is also found that the optimum MTMD and MTMD(II) can maintain the same level of the robustness and the effectiveness is somewhat lower for the optimum MTMD than for the optimum MTMD(II).

Key words: MTMD, MTMD(II), Min.Min.Max.DMF, optimum parameters, ground acceleration