Library / Mechanical / MEC-28
Mechanical
Base-excitation transmissibility
Ratio of mass motion to support motion for a vibrating base.
- Ref
- MEC-28
- Rev
- v1
- Field
- Mechanical
- Result
- X/Y
For harmonic base displacement of amplitude Y, X is the absolute motion amplitude of the mass. The ratio tends to one at very low frequency and equals 1 at r = √2 for every damping ratio. Isolation (X/Y < 1) needs r > √2.
A soft mount can shield equipment from shaking if the shaking is much faster than the mount’s natural frequency.
Calculator
- Isolation efficiency 1 − X/Y64.41 %
- Crossover ratio √21.414
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- With ζ = 0.1 and r = 2 only about 36% of the base motion reaches the mass: isolation efficiency about 64%.
- Below r = √2 an isolator amplifies vibration instead of reducing it.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing () | Local step | Change in result |
|---|---|---|---|---|---|---|
| r Frequency ratio | 1.5 to 5 | 0.05887 | 0.8122 | 0.7533 | +10% | −20.6 % |
| ζ Damping ratio | 0.01 to 1 | 0.3336 | 0.8246 | 0.4911 | +10% | +1.25 % |
Sweep of Frequency ratio
| Frequency ratio | Transmissibility |
|---|---|
| 1.5 | 0.8122 |
| 1.938 | 0.3856 |
| 2.375 | 0.2373 |
| 2.813 | 0.1655 |
| 3.25 | 0.1244 |
| 3.688 | 0.09846 |
| 4.125 | 0.08084 |
| 4.563 | 0.06824 |
| 5 | 0.05887 |
Sweep one variable
Variables and how each one contributes
Transmissibility
What the equation gives you. Everything else feeds it.
Damping ratio
Fraction of critical damping. Above r = √2 extra damping makes isolation worse.
Frequency ratio
Base frequency divided by natural frequency. Higher r gives better isolation.
Worked example with the values above
- (2ζr)² = (2 × 0.1 × 2)² = 0.16.
- Numerator: 1 + 0.16; denominator: (1 − 4)² + 0.16.
- X/Y = 0.3559.
Assumptions and limits
- Linear mount with viscous damping.
- Single-degree-of-freedom model.
Common mistakes
- Choosing a stiff mount that puts r below √2.
- Adding damping to improve high-frequency isolation.
Statistics and uncertainty
Frequency ratio uncertainty of ±10% changes the transmissibility by roughly ±25% near r = 2, so design with margin.
Where it is used
- Equipment shock and vibration mounts.
- Vehicle and vessel isolators.
Maths you need
- Frequency ratio: r = ω/ωn
- Damping ratio: ζ