Torsional Vibration
The fundamental torsional natural frequency of a shaft. A drive train that sits on a torsional resonance will fatigue a coupling or a gearbox long before it fails in steady torque.
| Length (m) | Frequency (Hz) |
|---|---|
| 0.5 | 3172.3 |
| 1 | 1586.2 |
| 1.5 | 1057.4 |
| 2 | 793.1 |
| 3 | 528.7 |
f = (1/2L)·√(G/ρ) · Free–free torsional mode.
c = √(G/ρ) · About 3,170 m/s for steel.
A clear path from inputs to results.
The fundamental torsional natural frequency of a shaft. A drive train that sits on a torsional resonance will fatigue a coupling or a gearbox long before it fails in steady torque.
How to use
- Set shaft length (m).
- Set diameter (mm).
- Set shear modulus (gpa).
- Set density (kg/m³).
- Read the headline metrics, then check the table for the detail.
The formula
Reference: Free–free torsional mode of a uniform shaft.
Worked example
At the default inputs
- Shaft length (m): 1.2; Diameter (mm): 60; Shear modulus (GPa): 79; Density (kg/m³): 7850
- 1
Fundamental frequency: 1321.8 Hz · Wave speed: 3172 m/s · Polar moment: 127.23 ×10⁻⁸ m⁴ · Critical speed: 7.931e+4 rpm
Fundamental frequency: 1321.8 Hz · Wave speed: 3172 m/s · Polar moment: 127.23 ×10⁻⁸ m⁴
Interpreting the result
A 1.2 m shaft rings at 1322 Hz, or 7.931e+4 rpm.
Assumptions & limitations
- Uniform shaft, free ends.
- No attached inertia such as a flywheel.
Frequently asked questions
What changes with a flywheel?
A large inertia at one end lowers the frequency and adds modes.
How do I avoid resonance?
Keep the operating speed well away from the critical, or add a damper.
Methodology last reviewed 2026-10-22. Results are informational and not financial or engineering advice — see our disclaimer.