VIBRATION ISOLATION EXAMPLE

Suppose that you must install an electronic “black box” aboard a helicopter known to vibrate strongly, when cruising, at 10 Hz. Unfortunately, the electronic “black box” has a resonance at 10 Hz. Prolonged exposure to 10 Hz vibration is likely to damage your “black box.” How (without improving your “black box”) might you protect it??
Isolate the “black box”
Of course. Hooray. You have four sets of four isolators. Which set to use? Supporting your electronic “black box” they will resonate at 100 or 10 or 5 or 2Hz. Somewhat oversimplifying your problem, and pretending that your “black box” is an SDoF or single degree of freedom system, Figure 5.4.3 predicts how each set will serve.

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Figure 5.4.3 Which isolator?

Which isolators to use?
The four SDoFs have natural frequencies of 100, 10, 5 and 2 Hz, per blue circles. Troubling helicopter vibration is at 10 Hz, per red circles. Which isolator set wil best protect your “black box”?

The 100 Hz fn set of isolators (upper left, Figure 5.4.3) is too stiff and accomplishes nothing. Transmissibility (another word for magnification) is about 1.

The 10 Hz fn set of isolators (upper right, Figure 5.4.3) worsens the problem by about 10:1. Transmissibility is about 10.

The 5 Hz fn set of isolators (lower left, Figure 5.4.3) looks pretty good. Transmissibility is about 0.2.

The 2 Hz fn set of isolators (lower right, Figure 5.4.3) looks very good. Transmissibility is about 0.02.

Too soft
Unfortunately, those 2 Hz isolators are too soft for “the real world.”

Why? To achieve 2 Hz fn, static deflection δ must be about 2.45 inches or 62 mm. In straight and level flight, with only the 10 Hz vibration present, the 2 Hz isolators will “do the job”.

Helicopter maneuvers
But helicopter maneuvers (such as a hard landing) would cause a large downward excursion, large displacement of the “black box,” likely colliding with nearby structure. You can’t take that risk.
Be satisfied with 5 Hz fn. With forcing frequency 10 Hz an octave higher, transmissibility 0.2 should be satisfactory. Your “black box” will “feel” only about 1/5 as much vibration as does the electronics rack in which it’s mounted.