Bridge Torsional Flutter: Critical Wind Speed Lab (2D)

Flow & Structure

Wind speed (V) 19.0 m/s

Torsional stiffness (k) 9.0

Structural damping (c) 0.35

Playback speed 1.0×

Live Readout

Elapsed time

0.0 s

Twist amplitude

0.0°

Critical wind speed

— m/s

Growth / cycle

0.00%

How it works

The deck's torsional twist θ obeys a single damped-oscillator ODE, integrated here with fixed-step RK2 (midpoint) at 1/240 s sub-steps for stability regardless of frame rate:

θ'' = −k·θ − c·θ' + a·(V² − Vref²)·θ'
a = 0.0011 (aeroelastic coupling)
Vref ≈ 2.41 m/s (model constant)

The last term is genuine negative aerodynamic damping: above a wind-speed-dependent threshold it outweighs the structural damping c and the net damping coefficient flips sign. Solve c_eff = c − a·(V²−Vref²) = 0 for V to get the live critical wind speed shown above — exactly the value this page recomputes every time you move the stiffness or damping slider:

Vcr = √(Vref² + c / a)

Below Vcr the phase-space spiral winds inward (decay); at Vcr it neither grows nor shrinks; above Vcr it winds outward — genuine self-reinforcing flutter, not a scripted animation. The Gust button injects a one-off angular-velocity impulse so you can watch the same trajectory decay or diverge from a fresh disturbance without resetting the wind/stiffness/damping settings.

Deck pane — end-on view of the deck cross-section twisting by the live-integrated θ.
Phase portrait — θ vs θ′; a decaying oscillator spirals to the origin, a flutter-unstable one spirals outward.
Amplitude trace — peak |θ| per half-cycle on a log scale, so exponential growth or decay reads as a straight line.

Deck twist θ Phase portrait (θ, θ′) Amplitude envelope