Vortices shedding behind a body produce an oscillating side force. If the body is flexible, it vibrates. The classical design rule is simple: keep the shedding frequency away from the structure's natural frequency.
The rule is correct but incomplete.
Lock-in: the frequency adapts to the structure
As the shedding frequency approaches the natural frequency, the flow abandons its own frequency and locks on to the structure's — and that lock-in persists over a range of velocities. You therefore experience resonance not at a single speed but across a band.
The design consequence: "our operating speed is 15% away from the resonance speed" is not sufficient assurance. The width of the lock-in band depends on the structure's damping and mass ratio; for light, lightly damped structures the band is wide.
What sets the amplitude
The vibration amplitude varies inversely with a dimensionless mass-damping parameter. A light structure in a dense fluid (a slender tube in water) reaches far larger amplitudes. The same geometry can therefore be trouble-free in air and damaging in water.
Modelling
The problem is two-way coupled and transient; one-way mapping cannot show lock-in. See the fluid-structure interaction note.
The wake must be adequately resolved; a damped wake gives a low excitation force and makes the problem look absent. See the vortex shedding note.
Passive remedies
Usually the most practical route is to prevent shedding from being regular: helical strakes, a section that varies along the span, a perforated shroud. These increase drag but break lock-in by dispersing the oscillating force — it is a trade-off decision, and the analysis is used to measure the trade.
References
- Williamson, C. H. K. (1996). Vortex dynamics in the cylinder wake. Annual Review of Fluid Mechanics, 28, 477–539. DOI: 10.1146/annurev.fl.28.010196.002401
- Menter, F. R. (1994). Two-equation eddy-viscosity turbulence models for engineering applications. AIAA Journal, 32(8), 1598–1605. DOI: 10.2514/3.12149