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Wind and cables
A stay is a tensioned string: f = (1/2L) sqrt(T/mu). Vortex shedding forces it at f = St U / D with St = 0.2.
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Model checks
The science
What is modelled
Each stay behaves as a first-mode string of length L, tension T and mass per metre μ. The wind forces it with a coherent Strouhal-frequency drag oscillation; the deck is a single-degree-of-freedom oscillator that also shakes the stays. This is the same engineering approximation as the 3D page, not a CFD or fluid-structure solver.
Equations
- String frequency:
f = (1/2L) √(T/μ). - Shedding:
fs = St U / D, St = 0.20. - Modal oscillator:
q'' + 2ζω0 q' + ω0² q = (4/π) (½ ρ Cd D U² / μ) sin(ωs t). - At resonance the amplitude is
A = a / (2 ζ ω0²).
Checks run in the page
- Free vibration frequency against the string formula.
- Logarithmic decrement against 2πζ/√(1-ζ²).
- Steady lock-in amplitude against the analytic resonance amplitude.
Cable motion is shown exaggerated and capped at 0.45 m; the real hazard of rain-wind induced vibration is not modelled.
What to try
- Press Tune wind to resonance and watch the amplitude build up over a few time constants.
- Increase the damping ratio to 0.15 (like a stay with dampers) and compare the resonance peak.
- Raise the tension: all natural frequencies move up, so the resonant wind speed rises.