Presets
Playback
Wind and deck section
Speed, turbulence and aerodynamic properties of the deck.
Bridge structure
Span, cable sag, mass, natural frequency and damping.
Layers
Model checks
The science
What is modelled
A long-span suspension bridge deck in wind. The deck is a bluff body of depth D; the wind U separates at its edges and sheds alternating vortices (a Kármán street) at the Strouhal frequency fs = St·U / D. Each vortex gives an alternating lift on the deck, F(t) = ½ρU²·D·CL·sin(2π fs t) per metre (ρ = 1.225 kg/m³).
Deck response
The first symmetric heave mode sin(πx/L) is a one-degree-of-freedom oscillator for the mid-span displacement q: q'' + 2ζωn q' + ωn² q = (4/π)·F(t)/m. The factor 4/π projects a uniform load onto the mode. Driving exactly at fn gives q = (4/π)F0/(mωn²)·1/(2ζ). Lock-in therefore happens near Ures = fnD/St, and damping is the only thing that limits the amplitude.
Wind drag and cables
Mean drag per metre is FD = ½ρU²D·CD. The main cables carry the dead load w = m g; for a parabolic cable the horizontal force is H = wL²/(8d) and the tension at the tower is H√(1+(4d/L)²). The exact hanging cable (catenary) is solved numerically on the fourth graph for comparison.
Model checks on this page
(1) A full RK4 integration driven at resonance against the closed-form amplitude. (2) Energy balance in steady state: work done by the vortex force equals work dissipated by damping. (3) Parabola against the exact catenary cable force.
Honest simplifications
This is forced vortex-induced vibration only: the lift does not react to the deck motion, so the lock-in plateau, amplitude-dependent lift and the self-excited torsional flutter that destroyed the Tacoma Narrows Bridge in 1940 are not modelled. One vertical mode, uniform wind along the span, constant St and CL. The wake is drawn schematically; motion is magnified in the picture only (the readouts are true values). Real design relies on wind-tunnel section-model tests.
What to try
Press Lock-in: vortex resonance: the shedding frequency matches the deck's natural frequency and the heave grows. Switch to heavy damping and watch the amplitude fall by a factor of about 12. Slide the wind speed through the yellow line on the first graph to walk over the resonance peak. Pick Gusty storm to see drag and the shedding frequency follow the gusts. Move the sag ratio to see the cable force H rise as the cable gets flatter.