抄録
It is widely known that linear tuned mass dampers (TMDs) are not effective to the post-yielding response of buildings during earthquakes. To overcome the disadvantage of linear TMDs, this paper proposes hysteretic tuned mass dampers. The equivalent natural period of a hysteretic TMD could passively be tuned according to change of the degree of nonlinearity in steel buildings during earthquakes. The optimal design method of this type of TMDs, however, remains unclear. Therefore, the objective of this study is to clarify the optimal values and present a sophisticated design procedure without time history analysis.
In this study, steel buildings are assumed to have hysteretic dampers with normal bilinear hysteresis and moment resisting frames respond to ground motions within elastic range. The hysteretic TMD has also bilinear hysteresis. The hysteresis is approximately modeled as the Bouc-Wen differential model. For the dynamic interaction system between a TMD and building, two-degree-of-freedom (2DOF) systems are employed to analyze the behavior. The Lyapunov equation for the covariance matrix of responses is derived from this 2DOF system. Ground motions are represented as Gaussian white noise having a uniform power spectrum in frequency domain. All the responses are evaluated through the framework of stochastic analysis with an equivalent linearization technique.
The design properties for the TMDs are composed of strength, stiffness and post-yielding stiffness. The optimal values to decrease the peak displacement responses are of interest. For obtaining the optimal design properties, response surfaces are created in terms of the design properties. The response surfaces show that the optimal strength of TMDs gradually increases according to the increase of the peak response acceleration of buildings. However, higher strength than optimal strength does not change the seismic effectiveness so much. This optimal strength of a TMD is mainly governed by the mass ratio which is a ratio of the effective mass of a building to TMD. The explicit form of optimal tuning criteria is formulated with a equivalent linearization technique. Then, it is revealed that the tuning ratio for the post yielding stiffness should be a little smaller in order to improve the robustness concerning the effectiveness of a TMD against a wide variety of seismic intensity.
Finally, the estimation method for the peak displacement of steel buildings is proposed based on equivalent linearization and a response spectrum method. The proposed method with hand calculation predicts quite accurate results compared to time history analysis. Through this study, the hysteretic TMD is proved to have the capability of controlling seismic responses in a wide variety of the limit states of steel buildings.
