r4.06.02 Modal calculation by classical dynamic substructuring

Summary:

This report presents the theoretical bases of modal synthesis calculation methods. We start with the description of the transformation of RITZ and the modal recombination methods that result from it. Next, we present modal synthesis using classical techniques of substructuration and modal recombination.

First, we present the classical dynamic substructuring techniques of CRAIG - BAMPTON and MAC - NEAL.

The modal synthesis calculation tools implemented in Code_Aster are then reviewed. We will detail the modal calculation by substructuring then the harmonic response calculation and finally the temporal response calculation.

Dynamic condensation by dynamic macroelements is then presented in static substructuration.

The last section of this document presents the principle of residue-by-effort calculation, making it possible to assess the quality of a reduced model for a given calculation. The methodology developed for the quality indicator for modal calculation for generalized models is also detailed.

• 1. Introduction
• 2. Modal synthesis
  • 2.1. Transformation of RITZ
  • 2.2. Modal recombination
  • 2.3. Modal synthesis
  • 2.4. Connection conditions between substructures
  • 2.5. Elimination of linear constraints
• 3. Classical dynamic substructuring methods
  • 3.1. Introduction
  • 3.2. Craig-Bampton method
  • 3.3. Mac Neal method
  • 3.4. Interface mode method (so-called reduced method)
  • 3.5. Implemented in Code_Aster
• 4. Modal calculation by classical dynamic substructuring
  • 4.1. Introduction
  • 4.2. Dynamic equations verified by the substructures separately
  • 4.3. Dynamic equations verified by the global structure
  • 4.4. Implemented in Code_Aster
• 5. Harmonic response by classical dynamic substructuring
  • 5.1. Introduction
  • 5.2. Dynamic equations verified by the substructures separately
  • 5.3. Dynamic equations verified by the global structure
  • 5.4. Implemented in Code_Aster
  • 5.5. Conclusion
• 6. Transient response by classical dynamic substructuring
  • 6.1. Introduction
  • 6.2. Transient calculation by projection on the basis of substructures
  • 6.3. Transitional calculation on a global modal basis calculated by substructuring
  • 6.4. Comparative study of the two methods developed
  • 6.5. Implemented in Code_Aster
  • 6.6. Conclusion
• 7. Dynamic condensation by dynamic macro-elements in static substructuration
  • 7.1. Introduction
  • 7.2. Classical problem and principle of the method
  • 7.3. Full or reduced base condensation methods
• 8. Indications for the subsequent quality control of the scale model
  • 8.1. General case for a calculation on a reduced model
  • 8.2. Special case of calculating the modes of a generalized model
• 9. Bibliography
• 10. Description of document versions