      ALL TOOLS
      /
      VIBRATION ISOLATION
    

CALCULATOR SDOF · STEADY-STATE

Vibration Isolation & Transmissibility

How much of the base’s harmonic motion reaches the equipment — displacement transmissibility for a spring-mass-damper system under base excitation.

/ INPUT

EXCITATION FREQUENCY f

SUPPORTED MASS m

DEFINE MOUNT BY

DAMPING RATIO ζ {{ zetaStr }}

            0.01 · light
            0.40 · heavy
          

NAT. FREQ  fₙ

{{ fnStr }}

Hz

FREQ RATIO  r

{{ rStr }}

f / fₙ

TRANSMISSIBILITY  T

{{ TStr }}

X / Y · dimensionless

ISOLATION

{{ effStr }}

efficiency

TRANSMITTED

{{ transStr }}

of base amplitude

TRANSMISSIBILITY vs FREQUENCY RATIO CH1 ▸ T(r) OP {{ opChip }}

/ HOW IT WORKS THEORY · BASE EXCITATION

When equipment is mounted on a vibrating surface (floor, vehicle, building), the support undergoes harmonic base motion y(t) = Y sin(ωt). The mount — spring stiffness k and viscous damper coefficient c in parallel — controls how much motion reaches the equipment. The displacement transmissibility T = X/Y (equipment amplitude over base amplitude) is:

+ + + + \[ T = \frac{X}{Y} = \sqrt{\frac{1 + (2\zeta r)^2}{(1 - r^2)^2 + (2\zeta r)^2}} \] \[ f_n = \frac{1}{2\pi}\sqrt{\frac{k}{m}} = \frac{1}{2\pi}\sqrt{\frac{g}{\delta}} \qquad\qquad r = \frac{f}{f_n} \]

NOTATION

T Displacement transmissibility — ratio of equipment amplitude X to base amplitude Y (T < 1: equipment moves less than the base) r Frequency ratio — base excitation frequency divided by natural frequency, f / f_n (isolation requires r > √2 ≈ 1.41) ζ Damping ratio — c / (2√km), fraction of critical damping (dimensionless; typical mount range 0.05–0.15) f Base excitation frequency — frequency of the harmonic floor or support motion (Hz) f_n Undamped natural frequency of the mount–equipment system, ω_n / 2π (Hz) k Total mount stiffness — combined spring constant of all isolators (N/mm) m Equipment mass supported by the mounts (kg) δ Static deflection of mounts under supported weight, δ = mg/k (mm); equivalent way to specify stiffness

Below r = √2 the mounts amplify base motion, with resonance (r = 1) as the worst case. True isolation begins above r = √2 — the design target r ≥ 3 limits equipment amplitude to less than 13 % of the base amplitude for light damping.

BASE EXCITATION MODEL

⊕ ENGINEER’S NOTE

More damping tames the resonance peak during start-up but slightly raises T at high r — it reduces isolation in the operating band.

Choose ζ to safely survive resonance on the way up to operating speed, not to maximise steady-state isolation.

{{ calloutTarget }} ζ ≈ 0.05–0.15