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Vibration Transmissibility Calculator

Enter the forcing and natural frequencies to get transmissibility.

How it is calculated

The tool models an undamped spring mount with one degree of freedom. It first forms the frequency ratio r = fforcing ÷ fnatural, where the forcing frequency is how fast the machine shakes the mount and the natural frequency is how fast the mounted machine would ring by itself, both in hertz. Transmissibility is then TR = 1 ÷ |1 − r²|. TR is the fraction of the shaking force or motion that gets through; above 1 means amplification, below 1 means isolation. The note says the mount isolates when r is greater than √2 (about 1.414), and otherwise that there is no isolation. At exactly r = 1 (resonance) the undamped formula is unbounded, so the tool shows ∞ with a resonance warning. The natural frequency must be above zero and the forcing frequency cannot be negative. Damping is ignored, so real mounts behave differently near resonance.

Worked example

A machine runs at 30 Hz on mounts with a natural frequency of 10 Hz. The frequency ratio is r = 30 ÷ 10 = 3.000. Then r² = 9 and |1 − 9| = 8, so TR = 1 ÷ 8 = 0.125. This ratio is greater than √2, so the tool says the mount isolates. Only 12.5% of the force passes through to the structure, meaning 87.5% is blocked. With the same machine on stiffer mounts at 25 Hz, r would be 1.2, TR = 1 ÷ 0.44 = 2.273, and the mount would amplify.

Try this example →

Common mistakes

  • Mixing units, such as the machine speed in rpm and the mount frequency in Hz. Both fields are hertz, so 1800 rpm is 30 Hz.
  • Swapping the two frequencies. The ratio is forcing over natural, so reversing them gives r = 0.333 instead of 3 and the note then says there is no isolation.
  • Believing that a stiffer mount always protects better. Making the mount stiffer raises the natural frequency, lowers r and can move you into amplification.
  • Reading the ∞ result at resonance as a real number. When the two frequencies are equal the undamped formula is unbounded; real systems have damping and a finite but large peak.
  • Using the result for a heavily damped mount. The formula leaves damping out, so for rubber or damped isolators the real transmissibility above √2 is usually higher than shown.

About this calculator

Transmissibility (TR) measures how effectively a spring-type mount isolates a vibrating machine from the structure it sits on. For the simplest case — an undamped single-degree-of-freedom isolator — it depends only on the frequency ratio r, the forcing frequency divided by the mount’s natural frequency: TR = 1/|1 − r²|. This calculator takes the forcing and natural frequencies, computes r, and returns TR.

The formula splits isolation behavior into two regimes that every mechanical engineer designing an isolation mount needs to know: when r is less than √2 (about 1.41), TR exceeds 1 and the mount actually amplifies vibration rather than reducing it — resonance at r = 1 makes this worst — while for r greater than √2, TR drops below 1 and the mount begins isolating, with transmissibility falling further as r increases. This is why isolation mounts are deliberately designed with a natural frequency well below the machine’s operating (forcing) frequency, and why the calculator flags whether a given setup actually isolates.

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