EFFECTS OF INSTALLING DIRECTION OF TMDS ON SEISMIC RESPONSE REDUCTION OF CYLINDRICAL LATTICE SHELL ROOFS WITH VARIOUS MAGNIFICATIONS OF OUT-OF-PLANE STIFFNESS OF ROOF

Abstract

 TMD (Tuned Mass Damper) has the advantage that the damping effect can be obtained by the mass of 1 to 3% of structure. In addition, TMD is fit for the vibration control of spatial structures because it is possible to install TMD by a single supporting point. Therefore, there are many studies on spatial structures with TMDs. In almost these studies, installing direction of TMDs is downward in order to control the vertical responses subjected to input wave. It is expected that the response reduction effect will be affected by the vibration direction of TMD. However, there is no study that the installing direction of TMDs with higher response reduction effects is examined. From these backgrounds, the purpose of this study is investigation of seismic response control effects by plural TMDs which have various installing direction for cylindrical lattice shell roofs with various magnifications of out-of-plane stiffness of roof. In addition, the robustness of response reduction effects for deviation of installing angles of TMDs and the relationships between the natural period ratio R_T and the installing direction of TMDs with the highest response reduction effect will be investigated.

 The object structures are the cylindrical lattice shell roofs with supporting substructure with the size of gymnasium. The magnifications of out-of-plane stiffness of roof are varied to 10, 50 and 100 times based on the shell roof with proportioned sections by allowable stress design for temporary loading with safety factor of members ν=2.5 under dead load. The treated types of TMD are Double TMD and Quadruple TMD. Frequency ratios and damping ratios of TMDs are calculated by using the equations for optimum condition. The installing directions of TMDs are vertical, horizontal, normal, tangential and mode directions. The mode direction is the direction determined by eigen vectors at the positions for installing the TMDs. The methods of analyses are a natural vibration analysis, a modal analysis and a time history response analysis which takes the geometric nonlinearity into account.

 From the numerical results, it is concluded as follows.

 1) The response reduction effects are the highest when installing directions of TMDs are determined by the ratios of the horizontal x direction component and the vertical z direction component of the eigen vectors at installation points of controlled modes (the mode direction), regardless of the half open angle and magnifications of out-of-plane stiffness of roof.

 2) In the case of TMDs installed in a direction other than the mode direction, the direction with higher response reduction effects varies according to the natural period ratio R_T. When the natural period ratio R_T is smaller than 1.0 or 1.3, the direction with higher response reduction effects is normal direction. On the other hand, when the R_T is larger than 1.0 or 1.3, the direction is the horizontal direction.

 3) If the average of angular deviation from installing angles of the mode direction, which is the vibration direction with maximum response reduction effect, Σ_K^θ is within about 15 degrees, there is no influence on the response reduction effect.

 4) Regardless of half open angle, the installing angles of the mode direction are in a linear relationship with R_T. That angle differs depending on shape of the controlled vibration mode. And if the installing point and substructure move in the same direction, that angle can be obtained by the defined equation (26), if the installing point and substructure move in the opposite direction, that angle can be obtained by the defined equation (27).