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The efficiency of the tuned mass damper (TMD) to torsionally balance nonlinear asymmetric structures subjected to unidirectional seismic motion is studied. Two models are analyzed. The first consists of a one-story building with four nonlinear resistant planes (oriented in the direction of the seismic motion) and two elastic planes (perpendicular to the direction of the seismic motion) with a linear TMD. The nonlinear constitutive relation of each resistant plane is represented by a Bouc-Wen model, and the seismic motion is modeled as a stationary stochastic process. The stochastic analysis of a one story monosymmetric model is performed using the linear equivalent statistic technique. To validate these results, deterministic time-history analyses are performed in a multistory model subjected to high broad and narrow bandwidth seismic demands. The results show that in the case of torsionally flexible structures subjected to a broad bandwidth seismic motions, the TMD tends to tune with the equivalent linear frequency of the structure without TMD, where the deformation of the maximum response edge dominates and is optimally located in it. Besides, for a narrow bandwidth seismic motions, the TMD's optimal frequency is tuned with the dominant frequency of the seismic motions. For broad bandwidth seismic motions, the TMD's optimal frequency decreases as the inelastic incursion increase, whereas for the narrow bandwidth seismic motions, the level of nonlinearity does not affect optimal frequency. The torsional balance condition, in general, does not lead to an even distribution of the damage, being more effective in structures with low nonlinear demand. KEYWORDS asymmetric structures, nonlinear structures, stochastic analysis, torsional balance, tuned mass damper 1 | INTRODUCTION Several authors have studied the behavior of tuned mass dampers (TMDs), concluding that these do indeed reduce the response of the structures when facing wind and seismic events. [1][2][3][4] The first investigations studied the efficiency of the TMD applied to structures with linear behavior. 3,4 However, in practice, structures suffer damage when facing seismic events of medium and high intensities, which is why it is of great importance to study the behavior of structures with nonlinear behavior. As a result, several researchers have studied the effectiveness of the TMD in the behavior of an inelastic structure with a linear TMD. Those studies show that the use of TMD in structures subjected to seismic excitations has positive benefits due to the reduction of the damage. These studies were initially conducted on symmetrical structures. [5][6][7][8][9][10][11][12] In particular, Soto-Brito and Ruiz 5 investigate the influence of the motion on the efficacy of the TMD to reduce damage on a nonlinear 22-story-high structure, under high intensity seismic events. The results show that although the installation of a TMD on a nonlinear structure may not reduce the maximum displacement under severe seismic events, it can successfully perform under l...

The influence of the frecuency content of seismic excitations on the behavior of an optimal tuned mass damper (TMD) is studied in the context of a system with explicit consideration of soil-structure interaction. A stochastic analysis is made in the time domain for two random processes, one considering a broad bandwidth process (BBP) and other considering a narrow bandwidth process (NBP). A structure built over three different types of soil (soft, medium and hard) is considered. For the optimization of the TMD, the minimization of the ratio between the standard deviation of the displacement of the main structure with TMD with respect to a structure without TMD, is used as the target function. It is found that for seismic excitations with high frecuency content, the ratio of the TMD frequencies compared to the fixed base frequency of the structure approaches to 1 as the soil becomes more rigid. It is also observed that the TMD become tuned with the flexible base frequency for all soil types, producing perfect tuning for small mass ratios and detuning gradually for higher mass ratios. On the other hand, the TMD optimal damping ratio increases as the TMD mass ratio is higher, independently of the soil type. The TMD is more efficient for higher values of the TMD mass ratios, especially on soft soil. In structures built over flexible base, that are subjected to low frequency content excitations, the optimal TMD is tuned with the flexible base, independently of the type of soil and the fixed base period of the main structure. The TMD optimal damping is not sensitive to the flexible period for small mass ratios, and reaches its minimum value when it matches with the predominant period of the seismic event. On the other hand, the TMD reaches its maximum efficiency when it is tuned with the flexible period of the soil-structure system, and coincides with the predominant period of the seismic exitation and is higher on soft soil. A deterministic analysis is made using two seismic records, an artificial earthquake compatible with the Chilean code NCh2745 characterized by high frequencies content and other similar to the event in 1985 in Mexico, characterized by low frequencies content. It is seen that the optimal TMD is efficient controlling the response of the structure in all types of soil analyzed.

The behavior of the tuned liquid column damper (TLCD) is analyzed in the control of non-linear structures subjected to random seismic excitations. The structure is modeled as a system of one degree of freedom with incursion in the non-linear range. The Bouc-Wen hysteretic model is used to model the non-linear behavior of the structure. A stationary stochastic analysis is performed in the domain of the frequency. An equivalent statistical linearization was used for the analysis of the main system and the TLCD. The TLCD parameters considered for the optimization process were the frequency and the head loss coefficient. Two target functions were considered, (i) reduction of the main displacement of the system, (ii) reduction of the hysteretic energy. Two random processes were considered as seismic excitation, first a broad bandwidth process and secondly a narrow bandwidth process. The results show that for a broad bandwidth process, the TLCD tends to tune with the linear equivalent frequency of the system in the case without TLCD, while for the narrow bandwidth process, it tunes (TLCD) with the dominant frequency of the input. It is seen that the TLCD becomes detuned with regard to the frequency of the structure as the structure becomes more non-linear. It is also seen that the optimal tuning ratio of the TLCD is unsensitive to the mass ratio of the device and the main damping ratio of the system. It is also concluded that in case of flexible structures, the optimal head loss coefficient tends to be lower and increases with regard to its length ratio. It is seen that the effectiveness of the TLCD is greater for higher mass ratios of the device. In addition, it is found that the optimal TLCD becomes less effective as the structure enters the non-linear range, showing lower efficiency than what is seen in the literature for optimal TLCDs in linear structures.

In this paper, the behavior of a tuned mass damper (TMD), to torsionally control a linear structure subjected to seismic excitations, is investigated. The dynamic system is analyzed taking into account lateral-torsional coupling, soil-structure interaction, and the rotational components of the foundation motion. The system model consists of an asymmetrical structure, founded on a soil modeled as a homogeneous semi-space. A stationary stochastic analysis is performed in the time domain, and a double Clough-Penzien filter of broad frequency content is used to define the random process for the X and Y directions. The torsional balance criterion is employed for the optimization of the TMD design parameters. The influence of the plan static eccentricity over optimum TMD parameters' behavior is also addressed, taking into account the fixed base period, flexible period, torsional frequency ratio, and soil type. Compliance with the torsional balance is verified. The results show that the inclusion of the soil rotational component has a notorious influence on the optimum TMD parameters. Moreover, torsionally flexible structures founded on soft and medium soil show significant influence on the torsional balance.Finally, a transitory response analysis is carried out for a 15-story model, subjected to an artificial bidirectional earthquake with a broadband frequency content. The multistory model response validates the results derived from the stochastic analysis.

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Análisis de la eficiencia de un amortiguador combinado sintonizado con incertidumbre en los parámetros sometido a una excitación sísmica de alto contenido de frecuencias.