Vibration Reduction

A tuned mass damper (TMD)

This demonstration compares free vibrations of a SDOF system and a similar system with a tuned mass damper, and shows the effect of the tuned mass damper in free vibration.

Fig. 18-5: Comparison of vibration with and without a tuned mass damper

Fig. 18-5 shows a single degree of freedom (SDOF) system consisting of a mass and a spring attached to the left hand of a cross arm. The same SDOF system is attached to the right end of the cross arm and a smaller SDOF system has suspended from it. The smaller SDOF system, which is used as a tuned mass damper, has the same natural frequency as that of the main SDOF system. In other words, the ratio of stiffnesses of the two springs is the same as the ratio of the two masses.

Displace the two main SDOF systems downward vertically by the same amount and then release them simultaneously. It can be seen that the amplitude of vibration of the SDOF system on the left is greater than that of the one on the right. The tuned mass damper vibrates more than the mass to which it is attached. The vibration of the tuned mass damper applies a harmonic force to the SDOF system, which suppresses the movements of the main mass.

The effect of a tuned mass damper is most significant if a harmonic load is applied to the system with a frequency close to the natural frequency of the system.

A tuned-liquid-damper (TLD)

This demonstration compares free vibrations of two SDOF systems, one with and one without water, and shows the effect of a tuned liquid damper in reducing free vibration.

A tuned-liquid-damper (TLD) is basically a tank of liquid that can be tuned to slosh at the same frequency as the structure to which it is attached.

Two circular tanks are attached to the top of two identical flexible frames as shown in Fig. 18-6. The tank on the right is filled with some coloured water. The effect of water sloshing on the vibration of the supporting structure can be demonstrated as follows:

1. Displace the tops of the two frames laterally by similar amounts.
2. Release the two frames simultaneously and observe free vibrations of the two frames. The amplitude of vibration of the frame on the right decays much more quickly than that of the frame on the left.

The difference is due to the water sloshing in the tank and dissipating the energy of the system.

Vibration isolation

This demonstration compares forced vibrations of two glasses containing similar amount of water, one with and one without a plastic foam support, and shows the effect of base isolation.

A medical shaker can be used as a shaking table to generate harmonic base movements in three perpendicular directions. A glass is fixed directly to a wooden board while a similar glass is glued to a layer of plastic foam which is mounted on the wooden board, as shown in Fig. 18-7.

Fill the two glasses with similar amount of water. When the shaker moves at a pre-set frequency, it can be seen that the water in the glass on the plastic foam moves less than that in the other glass. The difference is due to the effect of the plastic foam, which isolates the base motion and also produces a natural frequency of the glass-water-foam system which is lower than that of the glass-water system and is thus farther away from the vibration frequency.

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.

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.

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.

Tyres used for vibration isolation

Fig. 18-8 shows two tyres placed between the ground and a generator in a rural area of a developing country. The presence of the tyres reduced the natural frequency of the generator and moving it away from the operating frequency. Although the operators of the generator may not have known much about vibration theory, they knew from experience that the presence of the tyres could reduce the level of vibration.

The London Eye

Fig. 18-9: The London Eye

The London Eye is the largest observation wheel in the world (Fig. 18-9a). It was built by the River Thames in the heart of London, just opposite to the Palace of Westminster. The wheel has a height of 135m and carries 32 capsules which can hold up to 800 people.

In order to reduce vibrations in the direction perpendicular to the plane of the wheel due to wind loads, 64 tuned mass dampers were installed in steel tubes which are uniformly distributed around the wheel. One of these tubes is indicated in Fig. 18-9b. The relation between the tuned mass damper and the tube is illustrated in Fig. 18-10. A mass and a spring in the tube were designed with a natural frequency close to the natural frequency of the wheel in the direction perpendicular to the plane of the wheel. Plenty of room is available in the tube to allow large movements of the tuned mass damper. No excessive vibration of the wheel has been observed in this direction since it was erected [18.4]

The London Millennium Footbridge

A total of 26 pairs of vertical tuned mass dampers were installed over the three spans of the London Millennium Footbridge [18.5]. These comprise masses of between one and three tonnes supported on compression springs. The tuned mass dampers are situated on the top of the transverse arms beneath the deck. One pair of the

These tuned mass dampers would become effective if the footbridge experienced relatively large vertical vibrations, though such vibrations were not the primary source of the well publicised problems when the bridge first opened.