Lecture Notes on Rigid Body Modes in Model Analysis

Summary

In this lecture, we discussed how engineers perform model analysis to determine natural frequencies and mode shapes of structures. Focus was given to rigid body modes, which are modes with zero frequency representing rigid translation or rotation without distortion. Evaluation of these modes depends on the purpose and application of the simulation, where they can be either expected or undesired.

Key Points

Understanding Rigid Body Modes

• Rigid Body Modes: Represent rigid translation or rotation, occur with zero frequency.
• Importance: Their evaluation depends on whether they are desired based on the analysis goal.

When Rigid Body Modes are Undesired

• Example: Model analysis of a circuit board showing zero frequencies at the beginning could indicate issues.
  • Could signal insufficient constraint, typically due to improperly defined connections.
  • Common analysis mistake: localized deformation indicating poor connection.
• Resolution: Always check the initial contact status using the contact tool before solving.
  • Example in video showed using the contact tool to identify and address open contacts.

When Rigid Body Modes are Expected

• Free-Free Modal Analysis: Used when no boundary conditions are necessary (e.g., aircraft, satellites).
  • The first six natural frequencies are expected to be zero or near-zero.
  • These six modes represent three translational and three rotational rigid body modes.
• Grounding Checks: Used to check if an artificial internal constraint (grounding) is present.
  • System is run without supports to expect six zero-frequency rigid body modes.
  • Non-zero frequencies in this configuration could indicate the presence of grounding.

Demonstration: Handling Rigid Body Modes and Grounding

• Model Setup: Two-part system with non-uniform gaps tested for proper contact configurations.
• Procedures:
  1. Import and set up geometry and materials.
  2. Configure and check bonded contacts, looking for uniform gaps.
  3. Perform mesh generation and modal analysis without defined boundary conditions to assess rigid body modes.
  4. Adjust contact formulations if necessary (MPC formulation was used for better results in non-uniform gaps).
  5. Re-run the modal analysis with fixed boundary conditions to observe changes in modal results.

Final Thoughts

• The presence and evaluation of rigid body modes depend significantly on the intended use of the model analysis.
• Engineers need to decide based on the assessment whether these modes are suitable or should be rectified by modifying model constraints and contact settings.

Conclusion

Rigid body modes play a crucial role in the accuracy of model analyses in engineering. Understanding when and how to evaluate these modes is essential for achieving realistic and reliable simulation results. The correct handling of these modes can influence the overall effectiveness of structural analyses in various engineering applications.