基于质量均匀分布的新型MTMD设计模型

提出了刚度和阻尼保持常量但质量均匀分布的新型MTMD设计模型以控制基底加速度激励下结构的振动，结构用某一受控振型的降阶模型表示.利用数值优化技术，研究了MTMD的最优参数，讨论了它对MTMD有效性和鲁棒性的影响.MTMD参数包括：质量间隔、频率间隔、平均阻尼比、调谐频率比、总质量比和总数.MTMD的优化准则定义为结构最大动力放大系数的最小值的最小化.为进行比较，还考虑了刚度和阻尼保持常量但频率均匀分布的MTMD设计模型.数值分析表明，新型MTMD设计模型不存在近0最优平均阻尼比，而且这种新型MTMD设计模型和频率均匀分布的MTMD设计模型达到近似同样的有效性和鲁棒性.

New MTMD Design Model Based on the Mass Uniform Distribution

Multiple tuned mass dampers (MTMD),which keep the stiffness and damping constant and have auniform distribution of masses, are taken into account for attenuating undesirable oscillations of a structure underthe ground acceleration. The structure is represented by its mode - generalized system in the specific vibrationmode being controlled using the mode reduced - order method. The optimum parameters of the MTMD areinvestigated to reveal the influence of the important parameters on the effectiveness and robustness of the MTMDwith 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 statedas 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) witheach TMD being identical stiffness and damping coefficient but unequal mass, whose natural frequencies take on auniform distribution,is also taken into consideration. It is demonstrated that any further increase in the totalnumber 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 theoptimum MTMD and MTMD(Ⅱ) can maintain the same level of the robustness and the effectiveness is somewhatlower for the optimum MTMD than for the optimum MTMD(Ⅱ).