Statistical seismic performance assessment of tuned mass damper inerter

Abstract

Summary In this study, the robust optimum design of a recently developed passive control device, i.e., tuned mass damper inerter (TMDI) is investigated to control a 10‐story base‐excited shear building benchmark. The H2 and H∞ of three different objective functions (i.e., minimizing roof displacement, minimizing 7th‐story displacement, and maximizing the TMD stroke) are selected as objective functions for two different single and double inerter configurations. Optimum free vibration parameters of the TMDI (i.e., natural frequency and damping ratios) are calculated using a metaheuristic technique for two different structural damping values. Additionally, the performance of the optimum designed damper and its robustness under 25 far‐fault (FF) ground motions are assessed in the time domain with 12 different performance criteria (i.e., the mean and standard deviation of the maximum and norm of response histories for roof displacement, roof acceleration, and the total kinetic energy of the building). Based on current work, the best performance index for single TMDI for all three objective functions is the roof absolute acceleration, showing a maximum of 45% reduction in the mean maximum roof acceleration for 25 earthquake records. Therefore, the TMDI is most effective when the goal is to reduce the floor accelerations. The double inerter configuration shows approximately the same values for the performance indices for all three objective functions and demonstrates similar reduction for a single TMDI. However, it increases the robustness of the control method by adding redundancy and enhancing the performance for different combinations of inertance and mass ratios.

Enhanced motion control performance of the tuned mass damper inerter through primary structure shaping

“…Further, for relatively small CR values (less than about 3%), the TMD outperforms the TMDI (normalized free‐end displacement is higher than 100%). All the above observations agree with the trends reported in previous numerical studies examining various TMDI‐equipped lumped‐mass models of different benchmark building structures exposed to wind or earthquake excitations 21,25,26,28,31,33 . Hence, it is safe to conclude that these trends are applicable to any type of cantilevered primary structure, and it is always beneficial to connect the second terminal of the inerter as further away from the free end of the primary structure as structurally and economically feasible.…”

“…In the first instance, this consideration is practically useful as it leads to more lightweight vibration absorbers and, thus, more economical since the attached mass is proportional to the up‐front TMD(I) cost 26 . The consideration is also beneficial in applications where connecting the inerter much below the top of the structure is practically challenging such as in the case of tall buildings discussed in Wang and Giaralis 38 and Kaveh et al 28 In this respect, increasing the depth ratio R of the primary structure (or more generally designing the primary structure such that the flexural rigidity over mass ratio, EI ( x )/ m ( x ), reduces faster with height) widens the applicability of the TMDI over the TMD. As an example, note that for shape “IV” in Figure 9c, the critical CR value beyond which the TMDI outperforms the TMD is 7.4%, 5.1%, and 2.75% for depth ratios R = 1 (uniform), R = 2, and R = 5, respectively.…”

“…To this end, in recent years, the inertia property of the inerter, defined by Smith 15 as a linear massless mechanical element resisting relative acceleration through the inertance constant, has been leveraged to relax requirements for large secondary mass in suppressing the motion of dynamically excited civil engineering structures via passive dynamic vibration absorbers 16–21 . Among these absorbers, the TMDI, introduced by Marian and Giaralis, 22 was shown to outperform the conventional TMD for the seismic protection of fixed‐based buildings 18,23–28 and base‐isolated buildings, 29,30 as well as for mitigating wind‐borne vibrations in buildings 31–33 and wind turbine towers 34 . In this respect, it was found that the incorporation of an inerter to the TMD can lead to significant attached mass reduction since the inertance scales up practically independently of inerter device physical mass in actual device embodiments 15,35,36 .…”

A Comparative Study of the Optimum Tuned Mass Damper for High-rise Structures Considering Soil-structure Interaction

“…To increase the traditional TMD effects, tuned mass damper inerter (TMDI) was investigated to control a 10-story shear building benchmark [19]. The performance and robustness of the optimum TMDI under 25 far-fault (FF) ground motions were evaluated in the time domain with 12 different performance criteria and three different objective functions [20].…”

Inerter-Connected Double Tuned Mass Damper for Passive Control of Buildings under Seismic Excitation

“…The promising features of TMD render it a hot topic for research [7] and a reliable device for practical applications [8] in the structural control community. However, to deploy TMDs for seismic vibration control, the main shortcomings of TMDs, i.e., narrowband effectiveness, high detuning sensitivity and the dependence of its performance to the excitation frequency content should be resolved [9]. Therefore, in the past decade innovative modifications have been proposed to eliminate the aforementioned deficiencies [10][11][12].…”