What is transmissibility (TR)?

Transmissibility is the ratio of the output vibration amplitude (force or displacement transmitted to the base or equipment) to the input amplitude. TR = 1 means no change; TR > 1 means amplification; TR < 1 means attenuation.

What formula is used?

The standard SDOF force and displacement transmissibility formula: TR = √[(1 + (2ζr)²) / ((1 − r²)² + (2ζr)²)], where r = ω/ωₙ is the frequency ratio and ζ is the damping ratio.

At what frequency ratio does isolation begin?

Isolation starts at r = √2 ≈ 1.414, where TR = 1 for all damping ratios (except ζ = 0 which also passes through 1 there). For r > √2, TR < 1 and the system attenuates vibration.

Why does higher damping hurt isolation at high r?

Damping reduces the resonance peak (good) but also transmits more energy at high frequency ratios (bad). Very low damping isolates well at high r but produces a large resonance peak when r ≈ 1.

What is a typical damping ratio for engineering structures?

Steel structures: 0.01–0.02; concrete: 0.02–0.05; rubber isolators: 0.05–0.15; heavily damped systems: up to 0.3. Critical damping (ζ = 1) produces no resonance peak.

Vibration Transmissibility Calculator

Enter frequency ratio and damping ratio to compute vibration transmissibility and see the full TR vs r curve.

System Parameters

Frequency Ratio r = ω/ωₙ

Excitation frequency divided by natural frequency. Range: 0.01 – 4.0

Damping Ratio ζ (zeta)

0 = undamped, 1 = critically damped. Typical: 0.01 – 0.3

Transmissibility Ratio

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Enter values above

TR vs Frequency Ratio

r = 0 to 4, current r marked

Key Reference Points

r	TR	Regime

Summary

The Vibration Transmissibility Calculator computes the transmissibility ratio TR for a damped single-degree-of-freedom (SDOF) system using the classic formula that accounts for both the spring-mass and damping contributions. Enter the frequency ratio r (excitation frequency / natural frequency) and the damping ratio ζ to get the TR value and a full response curve. Use it to design vibration isolators, assess resonance risk, and understand the trade-off between damping and isolation performance.

How it works

Enter the frequency ratio r = ω/ωₙ (excitation frequency divided by natural frequency).
Enter the damping ratio ζ (0 = undamped, 1 = critically damped; typical structures: 0.01–0.2).
The calculator applies the SDOF transmissibility formula to compute TR.
TR > 1 means the output vibration exceeds the input (amplification); TR < 1 means attenuation.
The chart plots TR across r = 0 to 4 so you can see the full resonance peak and isolation zone.

Use cases

Determine if a vibration isolator will attenuate or amplify force at a given excitation frequency.
Select isolator stiffness to keep the system in the isolation zone (r > √2).
Assess resonance risk when the excitation frequency is near the natural frequency.
Compare damping levels to balance resonance peak height against isolation efficiency.
Validate analytical SDOF models against measured frequency response data.
Teach or study structural dynamics and vibration isolation concepts.

Frequently Asked Questions

Last updated: 2026-06-14 · Reviewed by Nham Vu