Model 4: A pendulum tuned-mass-damper

This demonstration shows the effect of a pendulum tuned-mass-damper on reducing vibrations at resonance. This effect has stimulated the use of a huge pendulum to reduce lateral vibrations of the 509m high Taipei 101 building.

A huge pendulum tuned-mass-damper is used in Taipei 101 to reduce the lateral vibrations of the building induced by wind or possible earthquakes. The principle of the vibration reduction can be demonstrated using a medical shaking table that can generate horizontal harmonic motion, two identical rulers to represent slender tall buildings and a string and a golf ball to model the pendulum.

    
a. The set-up of the test                                   b. The two structures
Figure 18.A1: A medical shaker and the test structures

Figure 18.A1 shows the set-up for the demonstration. The frequency of the movement of the shaker can be adjusted manually between 0 and 4 Hz. The two rulers (one with and one without a pendulum) are vertically placed on the shaking table and clamped at their lower parts using two horizontally placed members fixed to the shaker. Two identical small rulers are placed horizontally at the tops of the two rulers for hanging the pendulum and for making the two structures identical. It can be seen from Figure 18.A1 that the only difference between the two “structures” is that one is with and one without the pendulum – a string and a hollow golf ball. The length of the string is determined allowing that the pendulum has the same natural frequency as that of the cantilever ruler. The fundamental natural frequency of the cantilever is determined experimentally using the shaker when resonance occurs.

    
Figure 18.A2: Comparison of lateral vibration of two rulers with and without a pendulum

The efficiency of the pendulum tuned-mass-damper is demonstrated through the demonstration when the motion frequency of the shaker is close to the fundamental natural frequency of the ruler as shown in Figure 18.A2. It can be observed that:

• The ruler without a pendulum vibrates significantly and the magnitude of vibration is several times of that of the ruler with the pendulum.
• The pendulum vibrates more than the ruler where the pendulum is in place.

When sweeping the motion frequency of the shaker between 0 Hz and 4 Hz which cover the natural frequencies of the ruler-pendulum system, the phenomena of a two degrees-of-freedom system can be observed.