Tuned mass dampers (TMD) have been used for the reduction of building responses to wind loading in many high-rise buildings. An innovative and resilient base-isolated building with a large mass-ratio TMD is introduced here primarily for earthquake loading in which the large mass-ratio TMD is located at basement. This new hybrid system of base-isolation and structural control possesses advantageous features compared to existing comparable systems with a TMD at the base-isolation story. The TMD stroke can be reduced to a small level with the use of an inertial mass damper and its reaction can be limited to a lower level by detaching its connection to ground. The proposed hybrid system has another advantage that the TMD mass does not bring large gravitational effect on the building itself. It is demonstrated that the proposed hybrid system is robust both for pulse-type ground motions and long-period, long-duration ground motions which are regarded as representative influential ground motions.

The authors declare that they have no competing interests.

TH carried out the theoretical and numerical analysis of the proposed TMD system. KF helped the numerical analysis. MT strengthened the theoretical analysis. IT supervised the theoretical analysis and organized the research group. All authors read and approved the final manuscript.

There is an increasing need and interest of construction of high-rise buildings in urban areas. This trend will be accelerated in the future. High-rise buildings and super high-rise buildings are required to resist for various external loadings, e.g. wind and earthquake loadings. Enhancement of

Tuned mass dampers (TMD) are useful for the reduction of building responses to wind loading and are installed in many high-rise buildings all over the world (Soong and Dargush

Nevertheless, some attempts have been made on the introduction of large mass-ratio TMD mainly for earthquake loading (Chowdhury et al.

Recently large mass-ratio TMDs are investigated for base-isolated buildings (Villaverde

However there still exist several issues to be resolved, e.g. avoidance of excessive vertical load by large mass-ratio TMD, reduction of TMD stroke, reduction of TMD support reactions.

The purpose of this paper is to propose an innovative system of base-isolated buildings with a large mass-ratio TMD at basement. The most serious issue of effect of excessive vertical load due to large mass-ratio TMD on the main building is avoided by introducing the large mass-ratio TMD at basement which is made possible due to the large displacement of a floor in the base-isolation story near basement. Another issue of large stroke of TMD even in the large mass-ratio TMD is overcome by introducing inertial mass dampers in parallel to the spring-dashpot system in the TMD system.

Figure

Conventional model and unrealistic model with excessive vertical load

Proposed-1 model and Proposed-2 model

Consider a base-isolated building without TMD. This model is called a _{I}, _{I}, _{I} denote the stiffness, damping coefficient and mass of the base-isolation story in the BI model. Furthermore let _{1}, _{1}, _{1} denote the stiffness, damping coefficient and mass of the superstructure. The displacements of masses _{1} and _{I} relative ground are denoted by _{1} and _{I}, respectively. This model is subjected to the base ground acceleration _{g}. The equations of motion for this model can be expressed by

Recently some systems of a base-isolated building with large-mass ratio TMD have been proposed. Mukai et al. (

Consider an Imass TMD model and a NewTMD model as shown in Fig. _{2}, _{2}, _{2} denote the stiffness, damping coefficient and mass of the TMD system. _{2} indicates the inertial mass capacity of the inertial mass damper installed between TMD mass and ground in the Imass TMD model.

Base-isolated building models treated in this paper (

For later comparison, the Imass TMD model and the NewTMD model are explained in the following. The equations of motion for Imass TMD model may be expressed by

On the other hand, the equations of motion for NewTMD model may be presented by

The equations of motion for a base-isolated building with large-mass ratio TMD at basement may be expressed by

A base-isolated building, as shown in Fig.

The model parameters of BI Model, Proposed-1 Model and Proposed-2 Model as shown in Fig.

The superstructure is a 20-story or 50-story reinforced concrete building and is modeled into a single-degree-of-freedom (SDOF) model. This modeling into an SDOF model is thought to be appropriate in a base-isolated building. The equal story height of the original building is 3.5 m. The building has a plan of 40 × 40 m and the floor mass is obtained from 1.0 × 10^{3} kg/m^{2}. The floor mass in each floor is 1.6 × 10^{6} kg. The fundamental natural period of the superstructure with fixed base is _{1} = 1.4 s for a 20-story building and _{1} = 3.5 s for a 50-story building. The structural damping ratio is assumed to be _{1} = 0.02. The stiffness and damping coefficient of the SDOF model are computed by _{1} = 2_{1}_{1}/_{1} with the fundamental natural circular frequency _{1} = 2_{1}.

The mass of the base-isolation story is 4.8 × 10^{6} kg. The fundamental natural period of the BI model with rigid superstructure is _{I} = 5.0 s for the 20-story model and _{I} = 6.0 s for the 50-story model. The damping ratio of the BI model with rigid superstructure is _{I} = 0.1. The stiffness and damping coefficient of the SDOF model are computed by _{I} = 2_{I}_{I}/_{I} with the fundamental natural circular frequency _{I} = 2_{I}. As for TMD, the mass ratio _{2}/_{1} is set to _{2}/_{1} is set to _{s} = 0.06. The damping ratio is assumed to be _{2} = 0.3. The stiffness and damping coefficient of TMD are given by _{2} = 2_{2}_{2}/_{2} in terms of the natural circular frequency _{2} of TMD . The process of determining _{2} is explained in Section ‘

In this section, the procedure of determination of stiffness and damping coefficient of TMD for the proposed model, Imass TMD model and NewTMD model is explained. The tuning of TMD is performed by minimizing the response ratio

Determination of stiffness of TMD (tuning of TMD)

Let us assume the input ground acceleration as^{T} indicates the matrix transpose. The displacement response ratio _{I1} is the undamped natural circular frequency of the BI model.

Let us assume the simulated long-period ground motion in terms of circular frequency

Simulated long-period ground motion (

On the other hand, let us assume the simulated pulse-type ground motion as_{p} = 2_{p}. The maximum ground velocity is set to 0.91(m/s) (the maximum velocity of JMA Kobe NS 1995). The period of the pulse wave is specified in the range of 1.0 ~ 3.0(s) with 0.1(s) as the increment. Figure

Simulated pulse-type ground motion (

Figure

Response to simulated long-period ground motion

On the other hand, Fig.

Response to simulated pulse-type ground motion

It is meaningful to note that, while TMD is connected to the base-isolation floor in the proposed models (Proposed-1 model and Proposed-2 model), TMD is connected both to the base-isolation floor and ground in the conventional base-isolation-TMD hybrid system (Imass TMD model and NewTMD model). For this reason the TMD reactions become relatively large in Imass TMD model and NewTMD model.

Although the proposed system (Proposed-2 model) increases the building response under a long-period ground motion slightly compared to the system without an inertial mass damper (Proposed-1 model), the response is still smaller than that of a base-isolated building without TMD. In addition, the proposed system (Proposed-2 model) can reduce the TMD stroke under a long-period ground motion owing to the inertial mass damper. Furthermore, the proposed system (Proposed-2 model) can also reduce the TMD stroke under a pulse-type ground motion owing to the inertial mass damper.

It can be concluded that the proposed systems (Proposed-1 model and Proposed-2 model) can reduce the TMD stroke and TMD reaction effectively compared to the conventional NewTMD model and Imass TMD model for both long-period ground motions and pulse-type ground motions.

Since the friction on rail in the TMD system could affect the performance of the proposed control system, its influence has been investigated. Although the static friction behavior is usually different from the dynamic one, the static friction coefficient has been treated as the same as the dynamic one. In this paper, the friction coefficient 0.008 has been used. In order to simulate the friction on rail, an elastic-perfectly plastic relation has been utilized and the initial stiffness has been specified as 1.0 × 10^{10}(N/m).

Figure

Influence of friction on rail in Proposed-1 Model subjected to simulated long-period ground motion (20-story, input period

Influence of friction on rail in Proposed-1 Model subjected to simulated long-period ground motion (50-story, input period

Influence of friction on rail in Proposed-2 Model subjected to simulated long-period ground motion (50-story, input period

On the other hand, Fig.

Influence of friction on rail in Proposed-1 Model subjected to simulated pulse-type motion (20-story, input period

Influence of friction on rail in Proposed-1 Model subjected to simulated pulse-type motion (50-story, input period

Influence of friction on rail in Proposed-2 Model subjected to simulated pulse-type motion (50-story, input period

It can be concluded that, although the frictions of TMD mass on rail in the proposed systems reduce the TMD stroke for both long-period ground motions and pulse-type ground motions, those do not affect so much on the building response.

In the large mass-ratio TMD, the reduction of stroke of TMD is a key issue. Figure

Several proposed models and conventional model for TMD stroke reduction

Table

Design conditions on TMD parameters in several models for TMD stroke reduction

Proposed-1 Model as basic model | Proposed-1-1 Model (detuning) | Proposed-1-2 Model (increased damping) | Proposed-1-3 Model (increased TMD mass-ratio) | Proposed-2 Model (with inertial mass damper) | Imass TMD Model (conventional model with inertial mass damper) | |
---|---|---|---|---|---|---|

TMD mass-ratio | 10 % | 10 % | 10 % | 26.7 % | 10 % | 10 % |

Inertial mass damper ratio _{s} | – | – | – | – | 0.06 | 0.08685 |

TMD damping ratio _{2} | 0.3 | 0.3 | 0.535 | 0.3 | 0.3 | 0.3 |

Tuning ratio | 0.8780 | 1.2430 | 0.7540 | 0.7880 | 0.8850 | 0.8950 |

Figure

Response to long-period ground motion

Response to pulse-type ground motion

Response comparison among proposed models and conventional models under long-period and pulse-type ground motions

Proposed-1-1 Model | Proposed-1-2 Model | Proposed-1-3 Model | Proposed-2 Model | Imass TMD Model | NewTMD Model | |
---|---|---|---|---|---|---|

Long-period ground motion | ||||||

Deformation of base-isolation story | × | △ | ◎ | △ | ◎ | 〇 |

Top-floor absolute acceleration | × | △ | ◎ | △ | ◎ | • |

Deformation of superstructure | × | △ | ◎ | △ | ◎ | • |

TMD stroke | Similar reduction from Proposed-1 Model | |||||

TMD displacement relative to ground | × | ◎ | 〇 | 〇 | ◎ | ◎ |

Reaction of spring supporting TMD | × | ◎ | × | △ | × | △ |

Reaction of oil damper supporting TMD | • | △ | × | △ | × | △ |

Reaction of inertial mass damper supporting TMD | – | – | – | ◎ | × | – |

Pulse-type ground motion | ||||||

Deformation of base-isolation story | • | • | • | • | • | • |

Top-floor absolute acceleration | • | • | • | • | • | • |

Deformation of superstructure | • | • | • | • | • | • |

TMD stroke | ◎ | 〇 | • | ◎ | • | 〇 |

TMD displacement relative to ground | • | • | • | 〇 | ◎ | 〇 |

Reaction of spring supporting TMD | △ | ◎ | × | • | △ | △ |

Reaction of oil damper supporting TMD | △ | △ | × | • | × | × |

Reaction of inertial mass damper supporting TMD | – | – | – | ◎ | × | – |

◎: excellent performance, 〇: good performance, △: fair performance, ×: ordinary performance

•: small change from Proposed-1 model

Figure

Comparison with BI Model under pulse-type ground motion

Response comparison under pulse-type motion (comparison to Proposed-1 Model, comparison of inertial mass damper reaction in Imass TMD Model to Proposed-2 Model)

Figure

Response comparison under long-period ground motion

Response comparison under pulse-type ground motion (comparison to BI Model and Proposed-1 Model, comparison of inertial mass damper reaction in Imass TMD Model to Proposed-2 Model)

Table

It is important to investigate the sensitivity of the system response to the change of the frequency of long-period ground motions. When the input frequency of long-period ground motions changes from the resonant situation, the TMD stroke and the reaction in the TMD decrease. Furthermore it has been confirmed that the response reduction performance in the TMD stroke and the reaction in the TMD is high in the proposed system compared to the conventional systems.

The following conclusions have been derived.

In order to overcome the difficulties caused by the resonance of a base-isolated building under long-period ground motions and the ineffectiveness of TMD under pulse-type ground motions, a base-isolated building with a large mass-ratio TMD at basement has been introduced. This new base-isolated building system is also aimed at enhancing the earthquake resilience of high-rise buildings. The proposed hybrid system of base-isolation and structural control is effective for both long-period ground motions and pulse-type ground motions. This hybrid system possesses advantageous features compared to existing comparable systems with a TMD at the base-isolation story. The TMD stroke can be reduced to a small level with the use of an inertial mass damper and its reaction can be limited to a lower level by detaching its connection to ground. The proposed hybrid system has another advantage that the TMD mass does not bring large gravitational effect on the building itself because of the placement of TMD at basement.

The proposed system (Proposed-1 model) can reduce the building response under a long-period ground motion by 38 % compared to the base-isolated building and keeps the base-isolation performance under a pulse-type ground motion.

Although the proposed system (Proposed-2 model) increases the building response under a long-period ground motion slightly compared to the system without an inertial mass damper, the response is still smaller than that of a base-isolated building without TMD (BI model). In addition, the proposed system (Proposed-2 model) can reduce the TMD stroke under a long-period ground motion owing to the inertial mass damper. Furthermore, the proposed system (Proposed-2 model) can reduce the TMD stroke under a pulse-type ground motion owing to the inertial mass damper.

The proposed system (Proposed-1 model and Proposed-2 model) can reduce the TMD stroke and TMD reaction effectively compared to the conventional NewTMD model and Imass TMD model for both long-period ground motions and pulse-type ground motions.

Although the frictions of TMD mass on rails in the proposed systems reduce the TMD stroke for both long-period ground motions and pulse-type ground motions, those do not affect so much on the building response.

Part of the present work is supported by the Grant-in-Aid for Scientific Research of Japan Society for the Promotion of Science (No.24246095). This support is greatly appreciated.