How to Analyze Harmonic Response in FreeCAD FEM

Harmonic response analysis predicts how a structure behaves under continuous cyclic or vibrating loads across a range of frequencies. In FreeCAD, this dynamic structural evaluation is performed using the Finite Element Method (FEM) workbench powered by the CalculiX solver backend via modal superposition. This guide covers the complete workflow to configure geometry, extract modal parameters, set up steady-state dynamic loading, and interpret the resulting frequency response spectrum.

1. Model Preparation and Meshing

Begin by creating or importing your part into FreeCAD and switching to the FEM Workbench.

  1. Create an Analysis Container by clicking the yellow analysis icon.
  2. Select the solid geometry and create a mesh using either Netgen or Gmsh. For dynamic vibration studies, use second-order (quadratic) tetrahedral elements to avoid artificial stiffness and ensure accurate modal representations.
  3. Assign a material using the FEM Material for solid tool. Ensure the material definition includes both Young's Modulus and Density, as mass properties are mandatory for dynamic calculations.

2. Apply Boundary Conditions

Define constraints that reflect real-world mounting conditions:

  1. Use Constraint Fixed on faces or edges where the component is anchored.
  2. Apply structural loads (such as forces or pressures) that will act as the baseline amplitude for your harmonic excitation.

3. Run a Frequency Analysis

Harmonic response in CalculiX uses the modal superposition method, requiring natural frequencies and mode shapes to be determined first.

  1. Double-click the CalculiX solver object in the tree.
  2. In the solver properties, set Analysis Type to Frequency.
  3. Specify the number of eigenmodes to calculate. Capture enough modes to exceed your target excitation frequency range by at least 30% to 50%.
  4. Run the solver to confirm natural frequencies and ensure there are no unconstrained rigid-body modes.

4. Configure Steady-State Dynamics (Harmonic Loading)

Native FreeCAD GUI features focus primarily on static and frequency calculations, so steady-state dynamic parameters are applied through CalculiX input keywords.

  1. Select the CalculiX solver object and locate the Solver Control or Custom Keywords property.
  2. Insert the *STEADY STATE DYNAMICS CalculiX keyword block beneath the frequency extraction step.
  3. Define the excitation frequency range (minimum and maximum frequency in Hz) and the number of calculation intervals.
  4. Define structural or modal damping (such as *MODAL DAMPING specifying Rayleigh damping factors or direct damping ratios per mode) to prevent infinite displacement at resonance.
  5. Identify the amplitude and node set where the cyclic force acts using the *AMPLITUDE and *CLOAD or *DLOAD keywords.

5. Execute and Review Results

  1. Click Write .inp file in the solver panel to inspect that your frequency and steady-state dynamics blocks are written sequentially.
  2. Click Run CalculiX to execute the simulation.
  3. Once completed, load the results back into FreeCAD.
  4. Review the generated response data: inspect maximum displacement amplitudes, von Mises stresses, and phase angles across the evaluated frequency spectrum to locate critical resonant peaks.