Structural Engineering & Statics
where the load goes
Concept

Machine foundation — where it appears

A block carrying a machine whose unbalanced forces would otherwise reach the structure. Its design is a dynamics problem rather than a bearing one: the block's mass and the soil's stiffness set a natural frequency, and the aim is to keep the machine's running speed well away from it.

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

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

How much of a force a mount lets through, at three damping ratios. The force transmitted to the support divided by the force applied, against the ratio of the forcing frequency to the structure's own, at 2%, 5%, 20% of critical damping. Every curve passes through exactly 1 at a frequency ratio of root two, whatever the damping: below that ratio a mount amplifies what it was installed to isolate, and above it more damping lets more through.

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 Damping that is computed rather than measured. Radiation damping of a 2.5 m block on soil with a shear wave speed of 178 m/s, against how heavy the block is made — the horizontal axis is a multiple of the 150 tonne block drawn. At that mass the three modes are at 47, 29 and 13 per cent of critical. None of this is dissipation: the energy leaves as waves travelling away into the half-space, so the quantity is a geometrical coupling and it can be computed from the size of the footing, the density of the soil and its shear modulus. Every curve falls as the block gets heavier, because a heavier block moves less for the same wave field — which is the one counter-intuitive thing here: mass buys frequency and costs damping.

The damping that is radiated

Every response in this field is quoted with a damping assumption attached, because damping is measured rather than designed and the measurement has a factor of two in it. A machine block on the ground is the exception: its damping is not dissipation at all, and it can be computed from three numbers none of which is a material property of anything that dissipates.

dynamics · Vibration isolation

Named alongside it

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

DampingResonanceServiceabilityTransmissibilityVibration isolationFrequency ratioHalf-spaceInertia blockNatural frequencyRadiation dampingRockingShear modulus

All concepts