What is vibration transmissibility?

Vibration transmissibility T is the ratio of the response amplitude to the excitation amplitude in a vibration isolation system. T 1 means amplification is occurring, especially near resonance.

When does vibration isolation begin?

For an undamped system, isolation begins when the frequency ratio r = f/fn exceeds √2 ≈ 1.414. Below this ratio, the mount amplifies vibration. The T = 1 crossover at r = √2 holds for any damping ratio.

What is a good damping ratio for isolation?

Low damping (ζ = 0.01–0.1) gives better isolation at high frequency ratios but higher resonance peaks. Moderate damping (ζ = 0.1–0.3) limits resonance amplification at the expense of some high-frequency isolation.

How do I calculate isolation efficiency?

Isolation efficiency = (1 − T) × 100%. For example, T = 0.1 means 90% isolation. This metric is only meaningful when T √2).

What is the frequency ratio r?

The frequency ratio r = f/fn, where f is the forcing (excitation) frequency and fn is the natural frequency of the isolation system. The system response depends primarily on this ratio and the damping ratio ζ.

Free Engineering Tool — #013

Vibration Transmissibility Calculator

Calculate the transfer function T of a vibration isolation system. Enter forcing frequency, natural frequency, and damping ratio to get transmissibility and isolation efficiency.

SDOF System Transmissibility T Isolation %

Results

Transmissibility T

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Isolation Efficiency

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Frequency Ratio r

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Transmissibility (dB)

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Phase Angle

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Transmissibility of a SDOF System

For a single-degree-of-freedom (SDOF) system with viscous damping, the transmissibility ratio T is:

Where r = f / f_n is the frequency ratio and ζ is the damping ratio.

Key Regions

r < 1 — Below resonance: T ≈ 1 (no isolation)
r ≈ 1 — Resonance: T peaks (amplification)
r = √2 ≈ 1.414 — Crossover point: T = 1 regardless of damping
r > √2 — Isolation region: T < 1, vibration is reduced

Isolation Efficiency

Isolation efficiency is only meaningful when T < 1 (i.e., r > √2).

Phase Angle

Practical Example

Example — Machine on Rubber Mounts

Given: Forcing frequency = 50 Hz, Natural frequency = 15 Hz, ζ = 0.05

r = 50 / 15 = 3.333

T = √(1 + (2 × 0.05 × 3.333)²) / √((1 − 3.333²)² + (2 × 0.05 × 3.333)²)

T = √(1.111) / √(102.23 + 0.111) = 1.054 / 10.117 = 0.104

Isolation efficiency = (1 − 0.104) × 100 = 89.6%

⚠️ Note: This formula applies to SDOF systems. Real structures may have multiple resonances. Always verify with measurements.