Structural Engineering & Statics
where the load goes
Generator

The tuned-mass generator

Rendered here at the parameters it defaults to, with every essay that calls it — which is the same list as the blast radius of changing it.
3% of the mass, hung on a spring, against the peak it removesThe magnification of a structure with 1.0% damping, with and without a tuned mass damper of 3.0% of its mass, tuned to 0.9709 of its frequency with 10.5% damping of its own. The bare peak is 50; with the absorber the single peak becomes two of 7.34, a reduction to 15% — a factor of 6.8. The marked points at frequency ratios 0.923 and 1.044 are the fixed points: the response there is the same whatever damping the absorber is given, which is what makes the optimum a question with an answer. The absorber's own stroke at the worse of the two peaks is 29.57 times the structure's static deflection, and that stroke is what decides whether it fits.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

3 essays call tuned-mass. The drawing above is what it returns with no arguments at all; every call below passes it something, because a placement that passes nothing draws whichever member of the family the generator happens to default to rather than the one its essay argues about.

Where it is called

Changing this generator changes every one of these figures.

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 Dynamics

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.

 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 Dynamics

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.

 00.511.522.533.540510152025forcing frequency ÷ natural frequencyforce out ÷ force in√2 — nothing gained, at any damping2% damping5% damping20% damping Dynamics

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.

The library, page 4 of 4 — where tuned-mass sits