Structural Engineering & Statics
where the load goes
Concept

Modal damping — where it appears

The damping ratio of one vibration mode, as a fraction of the critical damping at that mode's own frequency. It decides how fast that mode's motion dies away and how large a resonance grows, and on a stay cable a damper near the anchorage caps it at the damper's distance over twice the cable's length.

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

What a damper at the anchorage can do, and the ceiling it cannot pass. Modal damping against damper size for a 200 m stay at 4500 kN, with the damper 4 m from the anchorage — 2.0 per cent of the length. Each curve is a mode, found as a complex root of the taut string with a viscous damper in it rather than from a formula. Every one of them peaks at 1.00 per cent of critical, which is x/2L exactly, and the peaks are at different damper sizes — a higher mode wants a smaller damper, because it moves faster at the same amplitude. The curves are flat near their peaks: half the optimum coefficient gives 80 per cent of the ceiling, and so does twice it.

The damper that is too near the end

A stay cable has almost no damping of its own, so it is given a damper — and the damper cannot go where the motion is, because the middle of a two-hundred-metre stay is a hundred metres above the road. What it can supply is then decided by one length, and no amount of damper changes it.

dynamics · Cable dynamics A link that keeps two buildings apart has made them one. The largest closing movement between a 500 t building with a 0.8 s period and a 300 t building with a 1.2 s period, 50 mm apart, under one 1.0 s sine pulse of 0.50 g, and each building's largest displacement, against the size of a viscous damper joining them across the gap, from 0.01 MN·s/m to 541.3 MN·s/m. With no link they close by 515 mm, and the stiffer building moves 220 mm and the softer 419 mm. The link that takes the most energy out, 0.64 MN·s/m, still lets them close by 214 mm. The least that keeps the 50 mm gap is 4.8 MN·s/m, where the stiffer building moves 269 mm and the softer 280 mm. At the largest link the two move together, 281 mm and 281 mm.

The damper that ends up as a joint

A damper across the gap between two buildings acts on exactly the motion the gap is sized for, and it can be sized for two different things. The size that takes the most energy out of the pair still lets the buildings collide. The size that keeps them apart has nearly stopped moving: it has joined them into one building, and the stiffer of the two pays for it in drift.

dynamics · Pounding

Named alongside it

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

DampingMode shapeViscous damperCable dynamicsEigenvalueEnergy dissipationFatigueNatural periodPoundingResonanceSeismic gapServiceability

All concepts