### Abstract

There are many examples of application of TMD. A high-rise building and a floor slab with large span in architecture field, a cable stayed bridge and a suspension bridge in civil engineering, for example. The response reduction effects in those examples are verified. TMD is fit for the vibration control of spatial structure because it is possible to install TMDs by a single supporting point. Therefore, there are many studies on spatial structure with TMD. The authors have verified the influences of the number and position of installed TMDs, the period and phase characteristics of earthquake motions and input direction of input wave on seismic response reduction effects. However, influence of free vibration characteristics of cylindrical lattice shell roofs on vibration control effects by plural TMDs have never been examined. From these backgrounds, the purpose of this study is investigation of seismic response reduction effects by plural TMDs for cylindrical lattice shell roofs which have different half open angles and ratios of natural period of supporting substructure to that of roof structure. First, the selection method of controlled modes which are larger contribution to response displacement subjected to earthquake motion is proposed by response spectrum analysis. Next, the reduction effects of maximum responses and the sum of square of vertical responses of all nodes at all steps of analysis by plural TMDs for cylindrical lattice shell roofs which have different free vibration characteristics are examined. The relationships between the natural period ratios R_{T} of the natural period of equivalent single mass system to that of antisymmetrical 1 wave mode of roof structure and response reduction factors are investigated. Finally, the response estimation by parallel multi-mass system substituted for shell structure with TMDs is attempted. From the numerical results, it is concluded as follows. 1) As plural TMDs are installed in all antinodes of controlled modes with larger contribution to the response displacements which are the locations that the reduction of responses for all nodes of structure is verified in references (18), (19), the responses reduce regardless of free vibration characteristics of cylindrical lattice shell roofs. 2) The response reduction effects by TMDs are higher as the sum of ratios of maximum vertical response of all controlled modes which are obtained from the response spectrum analysis is larger. On the other hand, the response reduction effects by TMDs are lower when the vertical response is smaller. 3) When the responses of the mode with natural period which is shorter than natural period of controlled mode occur in the positions for installing TMDs, the responses of the mode with natural period which is shorter than period of controlled mode reduce. 4) The reduction effects of response acceleration and response displacement are higher in the range of 0.5 < R_{T} < 1.25. On the other hand, the responses hardly reduce in the range of R_{T} > 1.25. Therefore, when TMDs are applied to cylindrical lattice shell roofs, it is necessary to consider not only the natural period of roof structure but also the ratio of natural period of supporting substructure to that of roof structure. 5) When the sum of effective mass ratios of controlled modes is larger, the response reduction factors of cylindrical lattice shell roofs by installing the TMDs can be estimated by the parallel multi-mass systems substituted for shell structure with TMDs..

Original language | English |
---|---|

Pages (from-to) | 1233-1243 |

Number of pages | 11 |

Journal | Journal of Structural and Construction Engineering |

Volume | 82 |

Issue number | 738 |

DOIs | |

Publication status | Published - Aug 2017 |

### Fingerprint

### Keywords

- Cylindrical lattice shell roof
- Free vibration characteristics
- Parallel multi-mass system
- Plural TMDs
- Response spectrum analysis
- Seismic response reduction

### Cite this

*Journal of Structural and Construction Engineering*,

*82*(738), 1233-1243. https://doi.org/10.3130/aijs.82.1233