Concept

Damping — where it appears

Whatever removes energy from a moving structure: friction in bolted joints, cladding rubbing against a frame, radiation into the ground.

Named by 9 essays across one field — each of them below, with the objects they name alongside it.

00.511.522.530510152025forcing frequency ÷ natural frequencyamplitude ÷ static deflection1% damping — 50× at the peak2% damping — 25.01× at the peak5% damping — 10.01× at the peak10% damping — 5.03× at the peak

The only thing that stops it

Drive a structure at its own frequency and the amplitude grows without limit unless something takes energy out. What takes it out is damping, and damping is the one structural property that is never designed, never drawn, and never known until the thing is built.

dynamics · damping
2345678910051015202530floor frequency (Hz)response factor1× pace2× pace3× pace4× pace4 Hz — R = 106 Hz — R = 7

The floor that is strong and unusable

A floor can satisfy every strength check, deflect less than the limit, and still be rejected by the people who work on it — because somebody walking across it at two steps a second happens to be exciting it at exactly the rate it likes to move.

dynamics · floor vibration
three structures · one recordT = 0.3 speak 12.54 mmT = 0.8 speak 46.2 mmT = 1.8 speak 108.95 mmpeak displacementperiod

The spectrum is not a load

A response spectrum looks like a load curve and is not one. Every point on it is the peak of a complete time integration of one particular structure, and the curve is what you get by doing that again for every structure there could be.

dynamics · response spectrum
10⁻³10⁻²10⁻¹10¹00.20.40.60.81frequency (Hz)n·S(n), scaled to its own peakthe structure, 0.2 Hza stiffer one, 2 Hzbackground — the structure following the gusts: 70% of the turesonant — the structure ringing: 90% of the responsegust factor on the mean response: 4.39

The wind is a spectrum

A wind load is quoted as a pressure, which suggests something steady. It is not — the energy is spread across four decades of frequency, almost all of it in gusts lasting minutes, and a tall building takes ninety per cent of its response from the sliver of that energy sitting at its own frequency.

dynamics · gust response
024681012141618200123shedding frequency (Hz)1.2 m across · St 0.18 · 0.9 Hzlock-in6 m/s02468101214161820050100150200wind speed (m/s)cross-wind amplitude (mm)0.40% damping — Sc = 11.2, peak 180.94 mm

The wind that brings its own frequency

Every other load in this subject arrives at whatever rate it happens to arrive at. Vortex shedding arrives at a rate set by the wind speed — so for any chimney, mast or cable there is always a wind speed at which the shedding matches the structure exactly, and it is a breeze rather than a storm.

dynamics · vortex shedding
020406080100120-0.015-0.01-0.0050.005people walking on the spantotal damping ratio0.60% damping · 0.5 Hz30.16 people — nothing leftbelow: a disturbance dies awayabove: the structure drives itself

The bridge that was pushed by its own sway

A crowd walking on a bridge that moves sideways adjusts its footing to stay balanced, and the adjustment pushes the bridge the way it is already going. The crowd is a damper with the sign reversed, and past a certain number of people the total damping is negative.

dynamics · crowd synchronisation
0.60.70.80.911.11.21.31.41.501020304050forcing frequency ÷ the structure's ownamplitude ÷ static deflectionno absorber — peak 503.0% absorber — peak 7.34a factor of 6.8, for 3.0% of the mass

The mass that helps by being late

Hang three per cent of a building's mass from a spring in its roof, tune the spring so the mass arrives a quarter-cycle behind the motion, and the peak response falls by a factor of seven. Nothing was strengthened and nothing was stiffened.

dynamics · tuned mass damper
00.511.522.533.540510152025forcing frequency ÷ natural frequencyforce out ÷ force in√2 — nothing gained, at any damping2% damping5% damping20% damping

The machine that shakes the building

Put a machine on springs to keep its vibration out of the floor, and below a frequency ratio of root two the springs make things worse. Every transmissibility curve ever drawn passes through exactly one at that ratio, whatever the damping — so a soft mount either works well or fails badly, with nothing in between.

dynamics · vibration isolation
024681012-0.01-0.0050.005wind speed (m/s)total damping ratio0.60% damping · 1.2 Hz4.14 m/s — nothing leftbelow: a disturbance dies awayabove: the structure drives itself

The motion that feeds itself

A steady wind contains no frequency at all, and it can destroy a bridge. The force that does it is manufactured by the structure's own movement, so there is no excitation to resonate with — there is a wind speed above which the equilibrium is unstable, and below which nothing happens.

dynamics · aeroelastic instability

Named alongside it

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

ResonanceServiceabilityAeroelasticityNegative dampingSelf excitationStability thresholdTuned mass damperAerodynamic admittanceAlong wind responseBase shearCritical velocityCross wind response

All concepts