Vibration Isolation Efficiency

Isolation efficiency is transmissibility wearing the clothes a specification writes in: $I = 1 - TR$, usually stated as a percentage. A transmissibility of 0.05 is 95% isolation. It carries no new physics whatsoever — it is the same number subtracted from one — and it exists because "95% isolation" communicates to a client and "TR = 0.05" does not.

The restatement does one genuinely useful thing: it makes the amplification case impossible to overlook. If $TR$ exceeds 1, the efficiency comes out NEGATIVE, and a report reading "−150% isolation" is very hard to sign off on, whereas "TR = 2.5" slides past. That negative number is the honest description of a mount installed below the $\sqrt{2}$ crossover: it is not defective, it is simply under a machine whose running speed sits too close to the mount's own natural frequency, and the cure is to change the ratio — a softer mount, added base mass, or a higher running speed.

The percentage flatters, and it is worth knowing how. Going from 90% to 95% isolation halves the transmitted force, but going from 95% to 99% halves it again and again — each step nearer 100% costs disproportionately more deflection, because the deflection needed grows as roughly the square of the frequency ratio. Above about 98% the equation stops being the binding constraint anyway. Rigid pipe, conduit, a grouted drain line, even a taut electrical whip will short-circuit the isolators completely; these flanking paths, not the mounts, set the result on any tightly specified installation, and flexible connectors on every single service are the whole difference between a design that works and one that only calculates.

Two more honest limits. This is a FORCE ratio, not a loudness ratio and not a felt-vibration ratio — 90% isolation does not make a room feel ten times quieter, because human perception of vibration and of structure-borne noise is closer to logarithmic. And the derivation assumes the supporting floor is rigid. A machine on an upper floor whose own natural frequency is near the machine's running speed can be perfectly isolated on paper and shake the building anyway, because the floor has quietly become the spring. On any long-span deck the floor's frequency belongs in the calculation next to the mount's.