Vibration Isolation Efficiency (ASHRAE)

The isolated system's natural frequency fn = 3.13/sqrt(static deflection in inches) Hz, the disturbing frequency = rpm/60, and the transmissibility T = 1/|(f/fn)^2 - 1| gives the isolation efficiency (1 - T). A 900 rpm fan on 1 in isolators runs fn 3.13 Hz, ratio 4.8, 95% efficient. The trap this flags: isolation needs a frequency ratio over sqrt(2) = 1.414 - a slow 200 rpm unit on the same soft mount sits near resonance and AMPLIFIES the shaking 7x, so the fix is a stiffer isolator. Undamped ASHRAE single-DOF idealization; the rated isolator deflection and the mechanical engineer govern.

fn = 3.13 / sqrt(static_deflection_in) Hz (= (1/2pi) sqrt(g/deflection), g = 386.4 in/s^2); f = rpm/60; ratio = f/fn; T = 1 / |ratio^2 - 1|; efficiency = (1 - T) x 100%; isolation requires ratio > sqrt(2).

ASHRAE Handbook -- Fundamentals, Sound and Vibration chapter, the single-degree-of-freedom vibration isolator (the classical Den Hartog transmissibility relation), by name.

The single-DOF isolator relations (natural frequency from static deflection, transmissibility, and isolation efficiency) are standard vibration theory published in the ASHRAE Handbook -- Fundamentals and every mechanical-vibration text; the arithmetic is public.

Estimate. AHJ and licensed professional govern.

Field names used by the API: equipment_rpm, static_deflection_in, fn_hz, disturbing_hz, ratio, transmissibility, efficiency_pct

• Natural frequency fn = 3.13 / sqrt(static deflection in inches) Hz, from (1/2pi) sqrt(g/deflection); the deflection is the isolator's rated value under the actual loadASHRAE Fundamentals, Sound and Vibration
• sqrt(2) threshold isolation occurs only when the disturbing frequency exceeds sqrt(2) x fn; below that the mount amplifies, with resonance at a ratio of 1; a stiffer isolator raises fnASHRAE Fundamentals, Sound and Vibration
• Undamped idealization the transmissibility neglects damping (which slightly reduces high-frequency isolation but limits the resonant peak); the disturbing frequency is taken as the running speedsingle-DOF vibration theory