Transmissibility⚠ unverified
Mechanical / Vibration Analysis · Compute the displacement transmissibility of a single-degree-of-freedom system
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| wn | wn | rad/s | 1.0 | Undamped natural frequency |
| omega | ω | rad/s | 1.0 | Excitation (forcing) frequency |
| zeta | ζ | — | 1.0 | Damping ratio (dimensionless) |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | TR | — | Displacement transmissibility ratio (dimensionless). Returns 0.0 when the denominator is non-positive |
The science & history
Understanding the Parameters
- $r = \omega/\omega_n$ — high $r$ (soft mount / high speed) improves isolation.
- $\zeta$ — more damping reduces the resonant peak but can worsen high-frequency isolation.
- $TR$ — force transmitted / applied force (or related displacement ratio for base motion).
Derivation (Approaching a Proof)
From the SDOF equations for force transmission through spring+damper to ground (or absolute response to base motion), the magnitude ratio of transmitted to applied amplitude is the displayed $TR(r,\zeta)$.
History
Transmissibility curves are the design chart for vibration isolation mounts and vehicle suspension concepts.
Related Concepts: Magnification Factor, Vibration Isolation Efficiency, Damping Ratio, Natural Frequency mass-spring
Notes: Registry calculator vibration-transmissibility (unverified). Classic SDOF isolator model.