Concept

Natural frequency — where it appears

The frequency at which a structure vibrates when disturbed and left alone, set by its stiffness against its mass, including the mass of fluid it carries with it. A load much faster than it is resisted by inertia, and a load much slower is resisted by stiffness alone.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Also named here as unsteady bernoulli — the same set of essays touches all of them, so they are one junction rather than several.

A bottom panel overshoots its static stress, and a lighter hull's panel is loaded less. The largest bending stress anywhere on the panel against time from first contact, for a 10° wedge entering at 5 m/s at constant speed and as free hulls of the full width's added mass and three tenths of it; solid, the panel's own response, dashed, the static stress the same pressure would give a massless panel. Constant speed: 361 MPa against 287 static; Hull = full width's added mass: 245 MPa against 195 static; Hull = 0.3 of it: 132 MPa against 106 static. The water reaches the panel at 4.5 ms and covers it at 11.2 ms at constant speed; the wetted panel's period is 7.84 ms.

A hull bottom feels the slam it has time to answer

The slamming pressure on a V-bottom is a narrow ridge at the spray root, a megapascal high, that sweeps across each panel of plating in a few milliseconds — about the panel's own period. So the panel neither feels the ridge's height nor ignores its speed: it overshoots the static stress by up to half, a rule that designs for the peak pressure asks for half as much plating again as it needs, and a light hull's slower, softer slam is gentler on its plating twice over.

inviscid · Unsteady bernoulli

On a flat bottom the plating's own give slows the water climbing it and takes a seventh off the slam; on a deep V, almost nothing. At the impact speed that loads the one-way panel to 200 MPa at each deadrise: left, the coupled panel's peak stress over the one-way panel's, against deadrise; right, the same against the panel's largest deflection over its rise across its width, w/(ℓ tan β). 4°: 2.27 m/s, ratio 0.847, deflection 3.99 mm; 6°: 2.9 m/s, ratio 0.894, deflection 4.24 mm; 8°: 3.44 m/s, ratio 0.934, deflection 4.44 mm; 10°: 3.94 m/s, ratio 0.972, deflection 4.61 mm; 15°: 4.99 m/s, ratio 1, deflection 4.81 mm; 20°: 5.8 m/s, ratio 0.983, deflection 4.69 mm.

Plating that gives way slows the water that slams it, but only on a flat bottom

The slamming pressure on a hull's bottom is a ridge that rides at the edge of the wetted width, and how fast that edge moves depends on how far the water has to climb. A panel of plating that bends inward under the load gives the water further to climb, and while it is moving away it slows the climb itself. Fed back into Wagner's condition, that takes a seventh off the peak stress of a panel on a four-degree bottom loaded to the edge of what aluminium can bear, and almost nothing on a deep V — because what matters is the plating's deflection against the bottom's own rise across the panel.

inviscid · Unsteady bernoulli

Named alongside it

The objects these essays reach for when they reach for this one.

Added mass Model limit Quasi-steady Slamming Unsteady bernoulli Aeroelasticity Free surface Impulse Measurement

All concepts