Damage Balance of Asymmetric Nonlinear Structures By Means of a Tuned Mass Damper

Abstract eng:
This research studies the effectiveness of a tuned mass damper (TMD) to balance the structural damage on asymmetric nonlinear structures subjected to a unidirectional seismic movement. Using the statistical and equivalent linearization technique, a model with three resistant planes with nonlinear behavior (oriented in the direction of the seismic movement) has been analyzed with a linear TMD. The nonlinear constitutive law of each resistant plane is represented by a Bouc-Wen element. The hysteretic energy of each plane normalized with respect to a symmetric structure without TMD is used as damage index, and it is equaled on the three planes to balance the damage over the asymmetric system. The design parameters of the TMD are obtained by equaling the hysteretic energy on the three planes. The results show that optimum response of the structure with TMD is very sensitive both to the frequency and the device position, and not to the damping of the TMD. In the case of structures subjected to an input of broad-bandwidth, the TMD tends to synchronize with the equivalent uncontrolled linear frequency, where dominates the deformation at the edge of maximum response. In contrast, for an excitation of narrow-bandwidth the optimum frequency of the TMD synchronizes with the dominant frequency of the excitation. Moreover, in broad-bandwidth processes, the TMD optimal location is over the edge with larger deformations under the uncontrolled condition, while for long period structures subjected to narrowbandwidth excitations, the TMD locates on the rigid edge. These positions are coincident with the edge where the most damaged plane is located, without TMD. In the case of broad-bandwidth processes balance of damage can only be achieved with low values of eccentricity (on average ), which is coincident with the position threshold condition of TMD within the floor section. Besides, in broad-bandwidth processes, as the inelastic incursion increases, the optimum frequency of the TMD decreases, while for narrow-bandwidth processes the TMD tunes the predominant frequency of the input, independently of the level of nonlinearity of the structure. Also, results suggest that increasing the nonlinearity level of the structure, the damage is simultaneously reached for a wide range of eccentricities. In general, the condition of uniform distribution of the damage normalized with respect to the symmetric system does not lead to a uniform reduction regarding the asymmetric system without TMD, being both the damage and the inelastic deformations lower over the plane closest to the location of the damper, thus producing an amplification in the rest of planes. Finally, the results show that for structures with decoupled torsional frequency ratio equal to 1, a natural balance of the reduction of hysteretic energy and the deformations with respect to the asymmetric system without TMD take place.

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