Vibration Analysis — validation & limitations

What this calculator checks and the method behind each result, the independent reference cases its engine is tested against, and what it does not check. Use it to decide how far you can rely on a result.

Open the Vibration Analysis

What it calculates

Standard / method: ISO 10816

ISO 10816-1:1995 Annex B, Table B.1 (vibration severity zone limits; superseded by ISO 20816-1:2016 — machine-specific limits moved to ISO 20816 Parts 2–8 and differ by part) · ISO 1940-1:2003, superseded by ISO 21940-11:2016 (only the form of an equivalent G value of the entered unbalance — no balance grade or tolerance is assessed) · MIL-STD-810H Method 516.8 (shock response spectrum)

SDOF free vibration — undamped/damped natural frequency, damping ratio, logarithmic decrement, and time-response plot with decay envelope
Forced vibration and resonance — dynamic magnification factor (DMF), amplitude, phase, quality factor Q, and near-resonance warning
ISO 10816 vibration severity zone classification (Classes I–IV, Zones A–D) from measured RMS velocity
Vibration isolation design — transmissibility, required isolator stiffness, static deflection, and mount-type recommendation
2-DOF eigenanalysis and complex FRF — two natural frequencies, mode shapes, and full receptance (mm/kN) frequency sweep
Dynamic vibration absorber (DVA/TMD) tuning — Den Hartog optimal mass ratio, stiffness, damping, and before/after FRF comparison
Rotor unbalance response with the equivalent G value of the entered unbalance on the ISO 1940-1 form (now ISO 21940-11; ladder G0.4 to G4000; not a grade assessment), Campbell diagram for critical-speed crossings, and shock response spectrum (SRS) to MIL-STD-810 via RK4 integration

Standards this tool applies

ISO 10816 — ISO 10816-1 (superseded by ISO 20816-1:2016) Annex B (Table B.1) class-ladder zone classification (Classes I–IV, Zones A–D) from measured RMS velocity, plus SDOF/2DOF natural frequency, forced response, isolation design, DVA tuning, Campbell diagram, and SRS.

Validation evidence — independent reference cases (1)

Each case runs the tool's engine on a worked example whose values come from a published source or a hand derivation from the cited equations, and an automated regression test asserts the engine against those values within the stated tolerance. "Conservative" means the engine is known to sit on the safe side of the reference and the test asserts that side. Sources are cited; their text is not reproduced.

Unbalance response amplitude and ISO 10816 severity zone
Agrees
Source: Rao, Mechanical Vibrations 5th ed. §3.7 eq. 3.83/3.84/3.89; ISO 10816-1:1995 (superseded by ISO 20816-1:2016) Annex B, Table B.1 typical zone boundary limits (Classes I–IV)
Inputs: M 200 kg, e 0.05 mm, fn 30 Hz, zeta 0.05, 1500 rpm; second case e 0.01 mm, fn 20 Hz, 3000 rpm
Quantity Reference value Tolerance
X peak case 1 (mm) 0.1096323 1e-6 relative
v_rms case 1 (mm/s) 12.17708 1e-6 relative
F_T case 1 (N) 781.7598 1e-6 relative
v_rms case 2 (mm/s) 2.641580 1e-6 relative
tests/golden/REF-vibration-unbalance-iso10816.golden.test.ts

Quantity	Reference value	Tolerance
X peak case 1 (mm)	0.1096323	1e-6 relative
v_rms case 1 (mm/s)	12.17708	1e-6 relative
F_T case 1 (N)	781.7598	1e-6 relative
v_rms case 2 (mm/s)	2.641580	1e-6 relative

Limitations

Not checked by this tool

Rocking and coupled modes of the mounted machine (6 degrees of freedom) — Single-axis model; for an offset centre of gravity analyse rocking and coupled modes
Flexible foundation or support structure — A rigid foundation is assumed; check the floor or frame natural frequency separately (e.g. /beams)
Non-linear mounts (amplitude-dependent stiffness and damping, creep) — Linear mounts; use the mount maker's dynamic stiffness data
Fatigue of the vibrating structure and mounts — Not computed; check the stress cycles with /fatigue
Structure-borne noise transmission — Transmissibility covers force only; acoustic isolation needs its own analysis

Results are engineering calculations for qualified users — see the disclaimer. Other tools: all validation pages · standards reference · symbols glossary.