Analysis–Test Correlation Example

A worked example comparing predicted and measured random vibration response — modal frequencies, response PSD and RMS — and diagnosing discrepancies.

Random Vibration5 min read

worked examplecorrelationanalysistestmodalRMSdiscrepancy

Problem

A random vibration analysis predicted a first mode at 85 Hz with RMS acceleration of 6.2 g at a response location. The test measured a first mode at 78 Hz with RMS acceleration of 8.1 g. Diagnose the discrepancy.

Given

FEA: fn = 85 Hz, a_rms = 6.2 g
Test: fn = 78 Hz, a_rms = 8.1 g
Damping assumed in FEA: 5%

Solution

Frequency discrepancy:
  Error = (85 − 78) / 78 = 9.0%
  This is larger than the 5% target — investigate mass/stiffness/BC

Possible causes:
  1. Over-stiff boundary conditions → fn too high
  2. Missing mass → fn too high
  3. Mesh too coarse → fn too high

RMS discrepancy:
  Ratio = 8.1 / 6.2 = 1.31 (test is 31% higher)

The frequency shift moves the resonance
closer to a PSD peak, increasing response.
Also, the test damping may be lower than
the assumed 5%.

If test damping = 3% (from modal survey):
  Miles ratio = √(5/3) = 1.29
  This alone accounts for most of the
  1.31× discrepancy.

Actions:
  1. Update boundary conditions to match test
  2. Update damping to measured 3%
  3. Re-run and check correlation improves
  4. Document the model update