Pedestrian-Induced Vibrations – Non-linear Feedback Response Analysis

An important step during footbridge design is to address the potential of unacceptable vibrations due to user activities on the deck. The existing methods are effective at estimating responses due to passing individuals; however predictions become less certain when applied to crowds. The difficulty has been in estimating the cumulative crowd loading. The proposed model simulates as close as possible the believed mechanism of interaction footbridge - pedestrians. Every person is simulated as a single object with its own properties and decision making matrix. Forces are transmitted at every step of movement along the deck. These forces will depend on individuals’ statistical properties and motions at the contact point. A set of rules to simulate the proposed non-linear, comfort based relationship have been formulated. Structural responses are calculated at every time step at the location of each individual. The contact force variations are adjusted depending on an algorithm of step alignment. When entering the bridge, pedestrians would start to impart forces. Over time, they may slow or quicken their gate depending on their interaction and level of comfort. The excitations would initially be out-of-phase and frequency both within the crowd and in relation to the structural motions thus the overall load would be a reduced sum of random forces. As people proceed moving on the bridge, depending on the feedback, may begin to alter their step, amplitude of motions, and phase. This feedback mechanism of people-bridge interaction would decide what is the force magnitude and level of correlation, and as a result, whether “lock-in” or “lock-out” would occur. Proposed mechanism assumes certain levels of comfort where individuals may start to feel a motion at a given frequency close to their own and tune to or, simply stop moving when these motions become intolerably high. The aim is at more realistic and less conservative predictions of the likely performance of footbridges under pedestrian loading. Examples of lock-in simulations are provided