Millennium Bridge (London) - Resonance

Resonance

The bridge's movements were caused by a 'positive feedback' phenomenon, known as synchronous lateral excitation. The natural sway motion of people walking caused small sideways oscillations in the bridge, which in turn caused people on the bridge to sway in step, increasing the amplitude of the bridge oscillations and continually reinforcing the effect. On the day of opening the bridge was crossed by 90,000 people, with up to 2,000 on the bridge at any one time.

Resonant vibrational modes due to vertical loads (such as trains, traffic, pedestrians) and wind loads are well understood in bridge design. In the case of the Millennium Bridge, because the lateral motion caused the pedestrians loading the bridge to directly participate with the bridge, the vibrational modes had not been anticipated by the designers.

The lateral vibration problems of the Millennium Bridge are very unusual, but not entirely unique. Any bridge with lateral frequency modes of less than 1.3 Hz, and sufficiently low mass, could witness the same phenomenon with sufficient pedestrian loading. The greater the number of people, the greater the amplitude of the vibrations. For example, Albert Bridge in London has a sign dating from 1973 warning marching ranks of soldiers to break step while crossing. Other bridges which have seen similar problems are:

• Birmingham NEC Link bridge, with a lateral frequency of 0.7 Hz
• Groves Suspension Bridge, Chester, in 1977 during the Jubilee river regatta
• Auckland Harbour Road Bridge, with a lateral frequency of 0.67 Hz, during a 1975 demonstration

After extensive analysis by the engineers, the problem was fixed by the retrofitting of 37 fluid-viscous dampers (energy dissipating) to control horizontal movement and 52 tuned mass dampers (inertial) to control vertical movement. This took from May 2001 to January 2002 and cost £5M. After a period of testing, the bridge was successfully re-opened on 22 February 2002. The bridge has not been subject to significant vibration since. In spite of the successful fix of the problem, the affectionate "wobbly bridge" epithet remains in common usage amongst Londoners.

An artistic expression of the higher-frequency resonances within the cables of the bridge were explored by Bill Fontana's 'Harmonic Bridge' exhibition at the Tate Modern museum in mid-2006. This used acoustic transducers placed at strategic locations on the cabling of the Millennium Bridge and the signals from those transducers were amplified and dynamically distributed throughout the Turbine Hall of the Tate by a programme which Fontana entered into the sound diffusion engine of the Richmond Sound Design AudioBox .