Multiple tuned mass dampers (MTMDs) distributed along height of a high-rise building are investigated for their effectiveness in vibration response control. A 76-storey benchmark building is modeled as shear type structure with a lateral degree of freedom at each floor, and tuned mass dampers (TMDs) are installed at top/different floors. Suitable locations for installing the TMDs and their tuning frequencies are identified based, respectively, on the mode shapes and frequencies of the uncontrolled and controlled buildings. Multimode control strategy has been adopted, wherein each TMD is placed where the mode shape amplitude of the building is the largest or large in the particular mode being controlled and tuned with the corresponding modal frequency. Newmark’s method is used to solve the governing equations of motion for the structure. The performance of the distributed MTMDs (d-MTMDs) is compared with single tuned mass damper (STMD) and all the MTMDs placed at top floor. The variations of top floor acceleration and displacement under wind loads are computed to study the effectiveness of the MTMDs in vibration control of the high-rise building. It is concluded that the d-MTMDs are more effective to control wind induced vibration than the STMD and the MTMDs placed at top floor.

The buildings are built taller, lighter, and slender as per modern world requirement, with the use of advanced technology, knowledge of new materials, and analysis software, which have assured safe constructions and comfort to human life. In the tall buildings, wind and earthquake borne vibrations are typically controlled by the use of tuned mass dampers (TMDs). The well-established concept of TMDs was originated since an attempt made by Frahm [

Multiple tuned mass dampers (MTMDs) have also been investigated widely for their effectiveness in vibration control. Iwanami and Seto [

For this study, a 76-storey benchmark building is considered, having 306.1 m height and 42 m × 42 m plan dimension. It is sensitive to wind induced loads because the aspect ratio (height to width ratio) is 7.3. The first storey is 10 m high; stories from 2 and 3, 38–40, and 74–76 are 4.5 m high; all other stories are having typical height of 3.9 m. Yang et al. [

Model of 76-storey benchmark building installed with (a) MTMDs all at top floor, (b) d-MTMDs along height of the building.

The governing equations of motion for the wind excited benchmark building installed with all MTMDs at top floor and installed with d-MTMDs are obtained by considering the equilibrium of forces at the location of each degree of freedom as follows:

Wind load is considered acting on the

The PSDF of the wind forces applied on building.

Figure

First five mode shapes of uncontrolled and controlled 76-storey benchmark building.

Figure

Flowchart for optimizing location and design parameters of d-MTMDs for wind response control of 76-storey benchmark building.

The first five modal frequencies to be controlled and frequency of each TMD are calculated as

Classical modal superposition technique cannot be employed in the solution of equations of motion here because the system is nonclassically damped owing to the difference in the damping in system with TMDs as compared to the damping in the system with no control. Therefore, the equations of motion are solved numerically using Newmark’s method of step-by-step integration, adopting linear variation of acceleration over a small time interval of

A comparison of wind responses is made for the linear model of the 76-storey benchmark building installed with the STMD, MTMDs all on top floor, and d-MTMDs. In Figure ^{2}, 0.155 m/s^{2}, 0.179 m/s^{2}, and 0.178 m/s^{2}, respectively. It is observed that the maximum reduction of top floor displacement is achieved when the d-MTMDs are installed as per the optimized location and design parameters (Figure

Time variation of top floor displacement and top floor acceleration for 76-storey benchmark building under wind forces.

Optimum number of dampers,

The first evaluation criterion for the controllers is their ability to reduce the maximum floor RMS acceleration. A nondimensional form of this performance criterion is given by
^{2} = RMS acceleration of the 75th floor without control.

The second criterion is the average performance of acceleration for selected floors above the 49th floor:

The third and fourth evaluation criteria are the ability of the controller to reduce the top floor displacements. The normalized forms of the criteria are given as follows:

To find the peak response of controlled structure normalized by the peak response of the uncontrolled building, the performance criteria

The performance in terms of the peak response quantities is also important in design of the system. This set of nondimensional performance criteria is defined as follows:
^{2}.

The variations of the performance criteria with increased number of TMDs for a chosen mass ratio are shown in Figure

Variation of performance criteria

To study the performance of the d-MTMDs the number of TMDs is increased up to five, with each controlling different modal response. The improvement in the performance criteria

From (

Time variation of the strokes of the STMD, MTMDs, and d-MTMDs.

Wind response control of a 76-storey benchmark building installed with nondistributed and distributed MTMDs as per modal frequencies and mode shapes is investigated. A comparison of the response of the buildings installed with the TMDs all at top floor and distributed along the height of the building (d-MTMDs) with optimized location and parameters is made. From the trends of the results of the present study, the following conclusions are drawn.

The installation of d-MTMDs is effective in significantly reducing the peak top floor displacement of the building under the wind excitation. The acceleration response is also controlled effectively by the d-MTMDs as compared to the STMD and MTMDs.

The installation of d-MTMDs in accordance with the modal properties, that is, modal frequencies and mode shapes, is more effective than the STMD and all TMDs installed on top floor.

The peak displacement response reductions in case of the STMD, MTMDs all at top floor, and d-MTMDs, respectively, are 15%, 40%, and 50%. The peak acceleration response reductions in case of the STMD, MTMDs all at top floor, and d-MTMDs, respectively, are 50%, 45%, and 45%.

The authors declare that there is no conflict of interests regarding the publication of this paper.