Isolator Static Deflection for a Target Isolation
The mount-selection inverse of the vibration-isolation tile: enter the running speed and the isolation efficiency you want, get the static deflection to specify. From T = 1 - efficiency, ratio = sqrt(1 + 1/T), fn = (rpm/60)/ratio, and deflection = (3.13/fn)^2 in. 90% isolation of a 900 rpm fan needs 0.48 in of deflection (a 4.5 Hz mount); tighten to 95% and it nearly doubles to 0.91 in - the softer the mount, the better the isolation, and this says how soft. Feeds straight back into the forward tile. Undamped single-DOF; the isolator selection and the mechanical engineer govern.
Formula and source
T = 1 - efficiency/100; ratio = sqrt(1 + 1/T) (> sqrt(2)); fn = (rpm/60)/ratio Hz; deflection = (3.13/fn)^2 in.
ASHRAE Handbook -- Fundamentals, Sound and Vibration chapter, the single-degree-of-freedom vibration isolator (the classical Den Hartog transmissibility relation) solved for the required static deflection, by name.
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