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.
Results
Transmissibility of a SDOF System
For a single-degree-of-freedom (SDOF) system with viscous damping, the transmissibility ratio T is:
Where r = f / fn 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
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.
Vibration transmissibility T is the ratio of the response amplitude to the excitation amplitude in a vibration isolation system. T < 1 means vibration is being isolated; T > 1 means amplification is occurring, especially near resonance.
For an undamped system, isolation begins when the frequency ratio r = f/fn exceeds √2 ≈ 1.414. Below this ratio, the mount amplifies vibration rather than reducing it. The T = 1 crossover at r = √2 holds for any damping ratio.
Low damping (ζ = 0.01–0.1) gives better isolation at high frequency ratios but results in higher resonance peaks. Moderate damping (ζ = 0.1–0.3) limits resonance amplification at the expense of some high-frequency isolation performance.
Isolation efficiency = (1 − T) × 100%. For example, T = 0.1 means 90% isolation efficiency. This metric is only meaningful when T < 1, i.e., when the frequency ratio r > √2.
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's dynamic response depends primarily on this ratio and the damping ratio ζ.
The procedures described on this page were developed and field-tested by the Vibromera team using the Balanset-1A, a portable dual-channel balancer and vibration analyzer for on-site rotor balancing.
Professional field balancing instruments and vibration analyzers. Measure transmissibility and isolation effectiveness on-site. Used in 50+ countries.
Nikolai Shelkovenko
Nikolai Shelkovenko is a vibration analysis engineer and the founder and CEO of Vibromera. For more than 15 years he has balanced rotating equipment in the field rather than on a test bench: mulchers, industrial fans, crushers, centrifuges, shafts and spindles. That work is what the Balanset instruments grew out of — they were designed as a tool a specialist can carry to the machine and use alone, on site, not as laboratory equipment. Vibromera was founded in 2017 and has been based in Porto, Portugal, since 2023. Development, assembly and support of the Balanset line all happen here. The flagship instrument is the Balanset-1A, a portable analyser for single- and two-plane balancing and for vibration diagnostics. Nikolai is personally involved in customer support, in working through difficult balancing cases and in the development of the software. He works with customers worldwide, in any language.
