How can resonance collapse bridges?

Many bridges and buildings have fallen down due to the effects of resonance – or to be more precise, mechanical resonance. This is the susceptibility of a structure to respond at an increased amplitude when the frequency of its oscillations matches its natural frequency of vibration. In other words, this means that if a structure begins to vibrate in a violent manner, it’s liable to fail mechanically and this can quickly lead to its total destruction.

Structures like bridges can start to oscillate – ie vibrate at a regular rate – for many reasons. Indeed, environmental factors like traffic, a high footfall or powerful machinery can
trigger vibrations. If these vibrations happen to occur at a system’s resonance frequency, then oscillation generates excitation at an atomic level, where more and more energy is stored. When this stored energy exceeds an object’s load limit, it will lose structural integrity.
One of the most famous examples of a resonance disaster is the 1940 Tacoma Narrows Bridge collapse in Washington, USA. This came about not simply as a result of mechanical resonance, but also aeroelastic flutter – a process that occurs when complex, varying oscillations are caused by passing winds.

This flutter only intensifies typical vibrations, heightening their amplification, which
makes building structures that are capable of resisting these forces even more difficult.
The effects of resonance are countered by installing tuned mass dampers, or harmonic absorbers.

These devices specialise in moving in opposition to the resonance frequency oscillations in a structure using springs, fluid or pendulums. The world’s largest tuned mass damper is a 660-ton pendulum in the Taipei 101 tower in Taiwan. This colossal, £2.5-million ($4-million) steel pendulum is found in the centre of the building from floor 87 to 91 and sways in opposition to the movement caused by high winds. Incredibly, the damper reduces overall movement by up to 40 per cent.

The London Millennium Bridge (pictured) is just one example of the effects of resonance and how it can be generated by a wide variety of factors. The bridge, which was seen to be wobbling not long after its opening in 2000, demonstrated a form of positive feedback – a synchronous lateral excitation to its structure. This was caused by the natural swaying motion of people walking across it – typically 2,000 pedestrians were on the bridge at any one time – with small sideways oscillations generated by people’s steps exaggerating and reinforcing existing motion. This resulted in a pronounced wobbling effect and the bridge was shut down later that year. Engineers had to counter the resonance-induced swaying effect by installing 37 fluid-viscous, energy-dissipating dampers to mitigate the horizontal movement and 52 tuned mass dampers to limit vertical movement. This refitting cost about £5 million ($8 million) and took over a year.