Table 3 Default parameter values used in the simulations. Here, S.D. is the standard deviation of parameter mismatch among pedestrians, which follows a normal distribution in all cases.
From: Emergence of the London Millennium Bridge instability without synchronisation
Parameter | Meaning | Units | Default value | Mismatch S.D. | Source |
---|---|---|---|---|---|
a | Auxiliary | m | 0.047 | 0 | |
\({b}_{\min }\) | Margin of stability | m | 0.0157 | 0.002 | Ref. 18 |
C | Bridge damping | Ns/m | 29,251 | ||
g | Acceleration of gravity | m/s−2 | 9.81 | ||
L | Effective leg length | m | 1.17 | 0.092 | Ref. 31 |
m | Pedestrian mass | kg | 76.9 | 10 | Ref. 31 |
M | Bridge mass | kg | 113,000 | Ref. 11 | |
pc | Auxiliary | m | 0.063 | 0 | |
Tadd | Pedestrian addition time | s | 20 | ||
X0 | Unperturbed half step length | m | 0.36 | ||
Y0 | Unperturbed half step width | m | 0.047 | Ref. 18 | |
λ | Damping due to walking | s/m2 | 23.25 | 0 | |
ω | Unperturbed angular | rad/s | 5.655 | 0.1 | |
Stride frequency | |||||
Ω | Angular bridge | rad/s | 6.503 | ||
Natural frequency |