Presets
Playback
Wind
Shedding frequency = 0.2 U / D.
Bridge
Frequencies follow from tension, mass and stiffness.
Layers
Model checks
The science
Modal model of the deck
The deck and main cables are modelled as a taut string with some bending stiffness. Its vertical mode shapes are sin(nπx/L) with angular frequencies:
ωn2 = (nπ/L)2 T/μ + (nπ/L)4 EI/μEach mode is a damped, driven oscillator: mn (ẋ̇ + 2ζωn ẋ + ωn2 x) = Fn sin(2π fs t), where mn = μL/2.
Wind forcing and resonance
Wind past the deck sheds vortices at the Strouhal frequency fs = St U / D (St ≈ 0.2) and the alternating lift force per length is about ½ ρ U2 D CL. When fs matches a natural frequency (lock-in) the steady amplitude is limited only by damping:
xmax ≈ Fn / (2 ζ mn ωn2)Only odd modes are excited by a uniform symmetric load, so modes 1 and 3 respond and modes 2 and 4 stay quiet.
Flutter
Above a critical wind speed the aerodynamic forces can add energy instead of removing it. The optional flutter switch lowers the effective damping to ζ0 (1 - (U/Ucr)2); when it turns negative the vibration grows until a cubic damping term limits it. This is a teaching caricature, not an aeroelastic derivation.
Honest simplifications
- Only vertical bending modes of a single span; torsion, which was decisive in the 1940 Tacoma Narrows collapse, is not modelled.
- Constant lift coefficient and Strouhal number; real values depend on deck shape and the wind direction.
- Linear structure; the flutter limiter is invented to keep the animation finite.
What to try
- Lock-in on mode 1: the shedding frequency equals f1 and the amplitude builds up for tens of seconds.
- Raise the damping slider and see the resonant peak in the wind-speed graph shrink.
- Lock-in on mode 3: the deck shows three humps.
- Slender deck, flutter: with flutter on and the wind above the critical speed the oscillation grows.