Tools · Structural dynamics
SDOF natural frequency & transmissibility
The mass-on-a-spring model behind most resonance checks. Find the natural frequency, then see how hard a forcing frequency drives it.
Typical damping: welded steel structures and piping 0.01–0.05; bolted structures 0.03–0.07.
| Natural frequency | |
| Quality factor Q = 1/2ζ (peak amplification) | |
| Dynamic amplification (force → displacement) | |
| Transmissibility (base → mass, or force → support) | |
| Separation from fn |
Transmissibility vs frequency ratio (log scale). The dot is your operating point.
The formulas
fn = (1/2π)·√(k/m) = (1/2π)·√(g/δst)
DAF = 1 / √((1−r²)² + (2ζr)²)
T = √(1 + (2ζr)²) / √((1−r²)² + (2ζr)²)
Below resonance (r < 1) the response follows the force. Near r = 1 it's amplified by roughly Q. Above √2·fn the transmissibility drops below 1, which is the principle behind vibration isolation.
For resonance avoidance, many design practices aim to keep natural frequencies clear of forcing frequencies by a margin, commonly around ±20% (for example in API 618 for pulsation-related piping mechanical response). Check the margin required by the standard you work to.