Torsional balance of nonlinear asymmetrical structures by means of a tuned mass damper

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 mono-symmetric 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.