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Vibration Analysis (Natural Frequencies)

Natural frequencies are best extracted from your global FE model of the structure. In Abaqus, this is done using a linear eigenvalue analysis set up in the Step Module.

Setting up the frequency step

  1. In the Step Module, create a new step
  2. Select Linear Perturbation > Frequency as the step type
  3. Set the number of modes you want to extract (start with at least 5–10 to capture the primary modes)
  4. Request Field Output for displacement (U) so you can visualize mode shapes in the results

Critical: density units

Density is the most common source of error in vibration analysis. Abaqus has no built-in unit system — you must use consistent units throughout.

In English units (lbf, inches):

The density value you look up (e.g., 0.06 lb/in³ for carbon/epoxy) is in pounds-mass per cubic inch. This must be converted to units consistent with lbf and inches, where:

Force = mass × acceleration
lbf = (lbf·s²/in) × (in/s²)

So the correct unit of mass is lbf·s²/in (also called a "slug" in the inch system).

Conversion:

density [lbf·s²/in⁴] = density [lbm/in³] / 386.09

For carbon/epoxy at 0.06 lbm/in³:

0.06 / 386.09 ≈ 1.554 × 10⁻⁴ lbf·s²/in⁴

Use this converted value in your Abaqus material definition.

Accounting for mass not in your FE model

Your global model may not explicitly include every internal component — brackets, fasteners, mechanisms, etc. However, their mass still affects natural frequencies. For vibration analysis, you must account for this missing mass by adding:

  • Point masses at known locations of concentrated mass (bolts, fittings, equipment)
  • Distributed mass spread over a region if the mass is more diffuse

In Abaqus, point masses are added via: Special > Inertia > Create > Point Mass/Inertia in the Property or Interaction Module.

Interpreting mode shapes

Thin-walled beam and wing structures typically exhibit global bending and torsion modes:

  • Lower modes — dominated by bending (out-of-plane deflection)
  • Higher modes — may involve torsion, in-plane bending, or local skin/panel modes

Visualize each mode shape in the Visualization Module to confirm the mode is physically meaningful and not a numerical artifact.

Quick checklist before running

  • [ ] Density is in consistent units (see conversion above)
  • [ ] All significant mass sources are included (point masses added if needed)
  • [ ] No rigid body modes are present (your model is properly constrained)
  • [ ] Field output for displacement (U) is requested so mode shapes can be visualized