Structural Engineering & Statics
where the load goes
Concept

Loss factor — where it appears

The fraction of a vibration's energy a material or device dissipates in one cycle, divided by 2π. For a lightly damped system it is twice the damping ratio, and it is the natural measure for dampers whose force does not follow velocity linearly.

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

A damper too large stops damping. The damping of a structure with 2.0% of its own, against the size of a viscous damper held by a brace — the damper's force over the brace's at the structure's own frequency, on a logarithmic scale — for braces a quarter as stiff as the structure, as stiff, and four times as stiff. With the brace at 0.25 the damping peaks at 7.9% for a damper of 0.86; with the brace at 1.00 the damping peaks at 22.7% for a damper of 0.58; with the brace at 4.00 the damping peaks at 63.9% for a damper of 0.29. Either side of the peak it falls: a small damper barely moves, and a large one barely strokes — it locks, and the brace carries the motion as a spring.

The damper is only as good as its brace

A viscous damper added to a frame is held by a brace, and the brace is a spring in series with it. That pair has a ceiling: the most damping it can add is (√(1+κ) − 1)/2, κ being the brace's stiffness over the frame's, reached at one damper size and lost on either side of it. A brace as stiff as the frame allows 20.7%; a quarter as stiff, 5.9%. A damper larger than the best one is not better — it strokes less, locks, and turns the brace into a strut that moves the resonance instead of flattening it.

dynamics · Damping Sized for one amplitude, a nonlinear damper damps only a band around it. The damping of a structure with 2.0% of its own and a brace as stiff as the structure, against the storey's amplitude over the amplitude the damper was sized for, on a logarithmic scale, for dampers whose force goes as the velocity to the power α, each sized to the brace's best at the design amplitude. All four give 22.7% there. The linear damper gives it at every amplitude. A tenth of the design amplitude, α = 0.5 gives 6.4%, α = 0.3 1.9% and α = 0.15 1.4%; a hundredth of it, 1.9%, 1.4% and 1.4% — below the structure's own, because the locked brace has stiffened it.

The damper sized for the earthquake

A fluid damper whose force goes as its velocity to the power 0.3 is chosen because it caps the force a large earthquake can push through its brace. The same exponent makes its effective size depend on how far it strokes. Sized to its brace's best at the earthquake's amplitude, it adds 20.7% of critical damping there, 5.4% at three-tenths of it, and nothing at all at a tenth — where the brace has locked, the building is stiffer, and the motion its occupants feel meets a resonance that is as sharp as an undamped frame's. Giving half the brace to a linear damper keeps 9.3% under the wind for 1.2 points at the earthquake.

dynamics · Damping

Named alongside it

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

BraceDampingNatural periodResonanceViscous damperEigenvalueNon-linear responseSeries stiffnessStiffnessWind load

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