Synchronous lateral excitation

File:Synchronous lateral excitation example.png|thumb|As the number of pedestrians on a footbridge increases (black line in steps), the lateral oscillations increase (gray area). After a critical number of pedestrians is reached (166 in this example), the bridge enters a stage of synchronous lateral excitation. Simplified graph based on page 37 of Parker, Matt. Humble Pi: A Comedy of Maths Errors. Penguin UK, 2019. The second is pedestrian-pedestrian synchronization, where individuals unconsciously align their stepping patterns, further reinforcing the resonant force. == Key cases ==

• The London Millennium Bridge experienced lateral vibrations up to 70 mm due to synchronous lateral excitation, requiring a £5M retrofit with dampers. • The Birmingham NEC Link bridge experienced a lateral frequency of 0.7 Hz. • The Toda Park Bridge in Japan is an early documented case (1990s) studied by Fujino et al., informing later synchronous lateral excitation models. == Mitigation strategies ==

Some ways to avoid synchronous lateral excitation are the implementation of tuned mass dampers, which were used in the Millennium Bridge to increase damping from 0.5% to 20% critical. Other strategies involve designing bridges with lateral frequencies outside the 0.5–1.1 Hz range as well as managing crows by limiting pedestrian density during events. == References ==