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VD-04Vibration & Structural Dynamics

Vibration Isolation

Transmissibility and isolation efficiency of resilient mounts - and the deflection you need.

Excitation

rpm
24.67 Hz

Isolator

mm
steel spring ≈ 0.005–0.01 · rubber ≈ 0.05–0.1 · air spring ≈ 0.1–0.2
%
Isolation efficiency
95.3%
Transmissibility
0.0475
26.5 dB
Frequency ratio r
4.95
Mount fₙ
4.98Hz
Target of 90% achieved.
Transmissibility curves
amplificationisolation√2target T = 0.1T = 0.04750.10.20.5125100.010.1110Frequency ratio r = f / fₙTransmissibility T
ζ = 0.05 (selected)ζ = 0.01 … 0.5
Required fₙ for target
7.44Hz
Required deflection
4.49mm
Required ratio r
3.32
§ Theory of operation

Transmissibility

A machine on resilient mounts forms a mass–spring–damper system. The fraction of the dynamic force (or base motion) that passes through the mounts is the transmissibility, a function of the frequency ratio r = f/f_n and damping ratio ζ:

\begin{aligned} T &= \sqrt{\dfrac{1 + (2\zeta r)^2}{(1 - r^2)^2 + (2\zeta r)^2}} \\ \text{Isolation efficiency} &= (1 - T) \times 100\,\% \qquad \text{Attenuation} = -20\,\log_{10} T\ \ \mathrm{dB} \end{aligned}

Three regions

  • r < 1: mounts behave as rigid - no benefit.
  • r ≈ 1: resonance - the mounts amplify vibration, limited only by damping. Machines must pass through this quickly at start-up.
  • r > √2: isolation begins. All curves cross at T = 1 there, regardless of damping.

Above √2, damping actually reduces isolation, which is why high-performance isolators use low-damping steel springs, with separate snubbers or dampers to control start-up resonance.

Sizing the mounts

For a lightly damped mount, the frequency ratio required for a target transmissibility T is r = \sqrt{1/T + 1}. Combined with f_n = 15.76/\sqrt{\delta}:

\delta_\mathrm{required}\,[\mathrm{mm}] = (\,15.76 \cdot r\,/\,f\,)^2

Typical design targets: 80–90 % for general plant, 95–98 % for equipment on lightweight floors near sensitive spaces. Remember that the supporting floor is itself flexible, the static deflection of the isolators should be at least 10 times the floor deflection.