Structural Engineering & Statics
where the load goes
Concept

Negative damping — where it appears

A force in phase with a structure's velocity rather than against it, so that the motion feeds itself and grows from any disturbance. It has a threshold rather than a magnification: below the critical wind speed the motion dies away and above it the motion grows without bound.

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

Also named here as stability threshold — the same set of essays touches all of them, so they are one junction rather than several.

The damping a crowd leaves behind, and the number of people that uses it up. Total damping ratio against pedestrians, for a structure with 0.60% of its own and a modal mass of 120 tonnes at 0.5 Hz. Each person walking laterally puts a force in phase with the deck's velocity into it — about 300 N·s/m per person — so the crowd subtracts from the damping, and at 30.16 people what is left is nothing. Below the threshold a disturbance dies away. Above it, the structure feeds itself and the motion grows out of nothing at all — which is what makes this a different mechanism from resonance rather than a severe case of it.

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 The damping a wind leaves behind, and the speed that uses it up. Total damping ratio against wind speed, for a structure with 0.60% of its own and a modal mass of 25 kg per metre at 1.2 Hz. The aerodynamic damping of a section whose lift falls with angle of attack is negative and grows with speed, so at 4.14 m/s what is left is nothing. Below the threshold a disturbance dies away. Above it, the structure feeds itself and the motion grows out of nothing at all — which is what makes this a different mechanism from resonance rather than a severe case of it.

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.

DampingSelf-excitationStability thresholdAeroelasticityCritical velocityCrowd loadingFlutterFootbridgeGallopingLateral vibrationTuned mass damper

All concepts