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Vibrations' mitigation of linear structures, subjected to random excitations, using linear tuned mass dampers (TMDs), has been widely adopted in the field of structural dynamics. Although the TMDs are reliable and constitute a very efficient low‐cost solution, their dynamic parameters should be carefully tuned in order to guarantee optimal performances. Several optimization methods can be used such as the reliability‐based optimization (RBO) of the TMD parameters. Even though the efficiency of the RBO strategy is proven, its main drawback shows up when addressing a multi‐degree of freedom structure. Indeed, only the targeted vibrating mode exhibiting the largest amplitude is controlled whereas the other modes, with relatively smaller vibrating magnitudes, remain uncontrolled. In the present work a new band‐limited BL‐RBO criterion is presented. The new criterion is based on the evaluation of the spectral moments of the structural response, which are required for the failure probability estimation, evaluated on a limited frequency band. The efficiency of the proposed method in controlling a 20‐storey shear building subjected to a seismic excitation has been compared to others from the open literature. It has shown good capabilities in performing a multimodal control of the vibrating structure with uncertainties. The robust multimodal control has been performed using several TMDs (two TMDs per resonant mode), mounted in parallel configuration, and the obtained results showed satisfactory attenuations in the vicinity of the targeted modes. [ABSTRACT FROM AUTHOR]

Summary: Tensegrity domes are reticulated prestressed structures composed of bars in compression and cables in tension. These structures are flexible lightweight systems with low structural damping, and thus, they are sensitive to vibrations induced by strong wind and earthquakes. The present work deals with the robust multimodal control of a large‐scale tensegrity dome of Geiger's type. Assuming random excitations and linear behavior of the structure around an equilibrium prestressed configuration, the control is achieved in the low‐frequency range using multiple tuned mass dampers (MTMDs). The optimal MTMD parameters, ensuring optimal performances, are obtained using a root mean square displacement (RMSD)‐based approach. The optimization strategy is firstly applied, in a deterministic context where the structural parameters uncertainties are not included, to control the fundamental resonant frequency of the dome structure and then extended to perform multimodal control using multiobjective optimization. In addition, in real‐life situations, it's very hard to describe actual engineering structures in precise model yielding to unavoidable internal and external uncertainties. To deal with these uncertainties, it has been shown that the proposed multimodal control is also able to carry out robust control in presence of structural uncertainties. The proposed optimization strategy applied to the dome structure is compared to other optimization strategies, from the open literature. The obtained results showed the efficiency of the proposed methodology of the passive control in both contexts, that is, the deterministic and the non‐deterministic where uncertainties are considered. [ABSTRACT FROM AUTHOR]

In this work a reliability based optimization (RBO) strategy of Tuned Mass Damper (TMD) parameters is presented. The strategy is based on an energetic approach. The strategy consists to optimize the TMD parameters so that we minimize the failure probability (objective function) characterized by the exceedence of the power dissipated in the primary structure of a certain threshold value during some interval time. The evaluation of the objective function is carried out using the classical Rice’s formula. The strategy is, firstly, applied to linear single-degree of freedom (SDOF) system, subjected to seismic motion, and then extended to linear multi-degree of freedom (MDOF) system. The use of the Rice’s formula requires the knowledge of the joint probability density function (PDF) of the considered processes; to this end, exact expression of the joint PDF is presented for the SDOF system and an approximation is presented for the evaluation of the failure probabilities for the MDOF system. By making use of the obtained joint PDF, for the SDOF system, as the a priori joint PDF, the approximation of the joint PDF, for the MDOF system, has been performed using the Minimum cross-entropy method (MinxEnt).To highlight the good effectiveness of the proposed strategy, a ten-story shear building, subjected to different earthquakes, is considered. The obtained results are compared with other from literature, and it has been shown the superiority of the proposed strategy. [ABSTRACT FROM AUTHOR]

This work deals with control of vibrating structures using tuned mass damper (TMD) in presence of uncertain bounded structural parameters. The adopted optimization strategy of the TMD parameters is the reliability based optimization (RBO) where the failure probability, approximated with the classical Rice’s formula, is related to the primary structure displacement. In presence of uncertain bounded structural parameters it is convenient to describe them using intervals. Consequently, the optimized failure probability is also defined over an interval. In this paper a continuous-optimization nested loop method (CONLM) is presented to provide the exact range of the optimum TMD parameters and their corresponding failure probabilities. The CONLM is time consuming; in this context an approximation method using the monotonicity-based extension method (MBEM) with box splitting is also proposed. Therefore, the initial non-deterministic optimization problem can be transformed into two independent deterministic sub-problems involving discrete-optimization nested loop rather than the continuous-optimization nested loop used in the CONLM. The effectiveness and robustness of the presented optimum bounds of the TMD parameters are investigated and a performance index is introduced. The numerical results obtained with a one degree of freedom and a multi-degree of freedom systems subject to different seismic motions have shown the efficiency of the proposed methods, even with high level of uncertainties. Besides, the good robustness of the TMD device when it is exactly tuned on the optimum TMD parameters corresponding to the deterministic structural parameters has been proven. [ABSTRACT FROM AUTHOR]