How does the anti-vibration device of a super-tall building like Taipei 101 work?

1.Tuning mass dampersRole in high-rise buildings:

The correct name for this large golden ball resembling a single pendulum inside 101 is the tuning mass damper (Tuned mass damper, referred to as TMD). The function of this damper is mainly to mitigate the vibration comfort problem caused by strong winds in the upper part of the building (related to the peak acceleration of the floor and not related to the floor displacement). According to relevant studies, when the floor acceleration reaches 50mm/s^2, some people will begin to feel the swing of the building and feel uncomfortable. Therefore, Taiwanese regulations stipulate that under the action of wind force during the return period of half a year (which occurs twice a year), the peak acceleration response of the top floor of the building shall not exceed 50mm/s^2.

In the early days of the 101 design, the scripturesWind engineering consulting companyAccording to RWDI analysis, the peak acceleration of the top floor under the action of wind during the half-year regression period reached 62mm/s^2, and further increased to 74mm/s^2 if the impact of typhoons was considered. Since the former has exceeded the specification limit, in order to solve the comfort problem caused by wind-induced vibration, the owner finally decided to install a damper on the top of the building. After installation, the acceleration of the top floor can be reduced by about 40%.

2. How Tuning Mass Dampers Work:

The working principle diagram of the quenching and tempering damper is as follows:

In the figure, m1, k1, and b1 represent the mass, stiffness, and damping of the main structure, respectively. TMD, on the other hand, is composed of a mass block/oscillator (mass m2, which provides inertial force), a spring (stiffness coefficient k2, provides recovery force), and damping (damping factor b2, which provides an energy dissipation mechanism).

When the main frequency of the main structure is excited by wind force, the TMD will produce a resonant behavior opposite that of the main structure due to the inertia of the oscillator and the recovery force generated by the spring. During the vibration process, part of the energy on the main structure will be converted into the kinetic energy of the TMD oscillator, part of it will be converted into the elastic potential energy of the spring, and the remaining part will be dissipated through the damper of the TMD. For this reverse resonance behavior, please refer to the rightmost animation in the gif below. Among them, the blue square represents the main structure, and the red square represents the TMD oscillator.

The reason why the control frequency of high-rise buildings is generally its fundamental frequency is because under normal circumstances, whether it is downwind (jitter) or crosswind vibration (vortex vibration), the response mainly comes from the first-order forced vibration of the structure, and the response from the higher order of the structure can be ignored.

Although the TMD in the 101 is a single pendulum, it works exactly the same. The only difference is that the recovery force of the TMD above is provided by the spring, while the recovery force of the monopendulum TMD is provided by the gravity of the mass block (similar to the old-fashioned wall clock at home). When the amplitude of a single pendulum is small, its self-oscillating period T is (where L is the pendulum length and g is the gravitational acceleration):

Since the control period of Building 101 is about 6.8 seconds, according to the above formula, the pendulum length L is about 11.5m for the TMD to be consistent with the control frequency/period. In addition to the four sets of 11.5-meter-long high-strength wire cables, considering the diameter of the spherical mass block is about 5.5 meters, it takes about five floors to place such a TMD. Therefore, the TMD is finally suspended between the 87th and 92nd floors of the building, spanning a total of 5 floors.

In the image below, eight large columns arranged diagonally below the mass blockHydraulic viscous damperIt is used to absorb and dissipate the kinetic energy of the mass block when swinging. The buffer steel ring directly below the sphere is fixed by eight anti-collision hydraulic dampers arranged horizontally, which is mainly used to prevent the mass block from swinging too much.

3. Changes in the dynamic characteristics of the main structure by TMD:

In essence, the reason why TMD can control the dynamic response (such as displacement, acceleration, etc.) of high-rise buildings is because the dynamic characteristics of the main structure at the control frequency have changed after the installation of TMD.

Taking the vibration damping analysis of a 305-meter super high-rise building at hand as an example, the control frequency of the high-rise is its fundamental frequency (f1=0.186Hz). The figure below shows the vibration damping measures without vibration reduction measures and after taking vibration reduction measures (with TMD andTMDI(only the fundamental frequency near 0.186Hz or 1.166rad/s is plotted). It can be seen that after the addition of TMD and TMDI, the absolute value of the frequency response function at the fundamental frequency of the high-level is greatly reduced. Due to the extremely simple linear relationship between the spectral density of the input (wind excitation) and the output (structural response) of the linear system (frequency response function), the absolute value of the frequency response function also means that the structure response at this frequency is reduced. To better understand this part, you can refer to the textbook on structural dynamics and stochastic theory and spectral analysis.

4. What other high-level management adopts similar vibration control devices:

There are too many examples, just to name two super-executives that everyone is familiar with:

1. Shanghai Tower (left):

2. Burj Khalifa Tower:

5. Tuned inertia damper / TMDI:

Finally, there was a wave of Amway.

Normally, to achieve the ideal vibration control effect, the vibrator mass of the wind damper generally needs to reach about 0.5%~1.0% of the mass of the main structure. For super high-rises, this is a very large mass. For example, the wind damper of Shanghai World Financial Center is 300 tons, the damper of Taipei 101 Building is 660 tons, and the damper of Shanghai Tower is 1000 tons. Obviously, it is very disadvantageous to place such a heavy vibration damping device on the top floor of a high-rise structure （not only poor economy, but also make super high-risesP-delta effectintensifying, etc.）.

In collaboration with universities such as Bristol in the United Kingdom and Sapienza University of Rome in Italy, our research group is trying to apply the Tuned Mass Damper Inerter （tentatively translated as "tuned inertial damping"）, which has been successfully applied to the suspension system of F1 cars, to high-rise structures. Judging from the current numerical analysis results of several high-rise buildings, TMDI can provide an additional vibration dampening effect of 8%-20% if the same quality of oscillators are used for wind-induced vibration. On the other hand, to achieve the same vibration dampening effect, the vibrator mass required for TMDI can be reduced to 60% of that of a conventional TMD, or even less! Unlike TMD, TMDI can even reduce the high-order mode response of high-level structures, and is not as sensitive to tuning as TMD （that is, when its frequency is different from the control frequency, it can still play a good vibration damping control effect）.