Structural Engineering & Statics
where the load goes
Concept

Resonance — where it appears

The condition of being driven at one's own frequency, where the response is bounded only by whatever damping the structure happens to have.

Named by 6 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 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 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

Named alongside it

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

DampingServiceabilityAerodynamic admittanceAeroelasticityAlong wind responseCross wind responseDamping ratioDetuningEnergy dissipationFixed pointsFloor vibrationFootfall

All concepts