Damped Vibration Isolation

Check force transmissibility for a linear single-degree-of-freedom isolator.

How this calculation works

Force transmissibility compares the amplitude transmitted through an isolator with the applied sinusoidal force amplitude. Enter the excitation frequency, the isolator system's undamped natural frequency and its viscous damping ratio. Damping is a fraction, so 0.1 represents a ratio of ten percent. The frequency ratio and damping together determine the steady force-transmission ratio. A result below one indicates reduced transmitted amplitude, while a value above one indicates amplification. The reported percentage is 100 times one minus transmissibility; a negative percentage therefore means amplification rather than isolation. Exactly undamped resonance has no finite result and is rejected. This single-mass linear model excludes startup transients, structural flexibility, additional modes and nonlinear mount behavior, and does not select or certify an isolator.

Inputs and units

Excitation frequency (Hz)
Undamped natural frequency (Hz)
Viscous damping ratio (1)

Method and formula

r = f/fn; TR = sqrt((1 + (2ζr)²)/((1 − r²)² + (2ζr)²)); amplitude reduction = 100(1 − TR).

Worked example

Example inputs

Excitation frequency: 30 Hz
Undamped natural frequency: 10 Hz
Viscous damping ratio: 0.1 1

Calculation steps

Calculate frequency ratio: r = 30/10 = 3, dimensionless.
Calculate the damping term: 2ζr = 2 × 0.1 × 3 = 0.6.
Evaluate force transmissibility: TR = sqrt((1 + 0.6²)/((1 − 3²)² + 0.6²)) = sqrt(1.36/64.36) = 0.145366, dimensionless.
Calculate amplitude reduction: 100 × (1 − 0.1453655301) = 85.463447%.

Example results

Frequency ratio: 3 1
Force transmissibility: 0.1453655301 1
Amplitude reduction (negative = amplification): 85.46344699 %

Assumptions

Linear single-mass spring-damper under steady sinusoidal excitation
Transmissibility is a force-amplitude ratio, not an energy reduction

Limitations

No startup transients, multi-axis modes, structural flexibility or nonlinear isolators
Does not select or certify mounts; zero damping at resonance is singular

Sources

West Virginia University: Vibration Suppression: Slide 8, force transmissibility for a damped isolator