Problem
Pedestrian bridges sometimes oscillate laterally when crossed by a crowd. Explain why the bridge’s natural damping (usually sufficient) can become insufficient when people unconsciously synchronise with the bridge’s own rhythm. Cite a well-known historical case and the technical solution adopted.
Solution
Normally pedestrians’ footsteps are uncorrelated: the lateral forces average out to almost zero, and the bridge’s intrinsic damping is enough to absorb them.
But if the bridge starts to oscillate laterally, people instinctively adjust their step to the motion to keep their balance: they synchronise with each other and with the bridge, driving it at its own natural frequency. This is resonance.
The energy fed in grows with amplitude (the more the bridge oscillates, the more people synchronise): a positive feedback that overwhelms the damping.
Historical case: the Millennium Bridge, London 2000, closed two days after opening. Solution: installation of viscous dampers and tuned mass dampers.
Links
Topics: Oscillations and simple harmonic motion Concepts: Resonance Skills: Analysis of limiting cases and thought experiments