v2.02.126 SDLL126 — Transient dynamic response of a beam with 3 disks, subject to the gyroscopic effect.

Summary:

In the case of a transient response, the objective is to validate the effect of the gyroscopic matrix on a beam supported at each of its ends, on linear supports. The beam is solid, has a circular cross section and has three disks. All calculations are carried out at a constant rotor speed.

There is no analytical reference for the transitory calculation. The comparison will therefore focus on the amplitudes and phases, in steady state, of the movements of the loading node obtained using three different methods.

Five calculations are therefore carried out:

• Calculus A: transient calculation in physical coordinates;

• Calculation B: transitory calculation in generalized coordinates;

• Calculation C: harmonic calculation in physical coordinates, tree according to \(X\);

• Calculation D: harmonic calculation in physical coordinates, tree according to \(Z\);

• Calculation E: harmonic calculation in generalized coordinates, tree according to \(Z\).

This problem therefore makes it possible to test the effect of the gyroscopic matrix that was developed for a straight beam and for discrete elements, in the case of a transient response.

The gyroscopic effect can introduce system instability. It is necessary to ensure that all modal amortizations are positive.

The results obtained by the various calculation methods are consistent with each other. The harmonic calculation was also validated using bibliographical references. The references are based on Timoshenko’s beam theory.

• 1. Reference problem
  • 1.1. Geometry
  • 1.2. Material properties
  • 1.3. Boundary conditions and loads
• 2. Benchmark solution
  • 2.1. Calculation method used for the reference solution
  • 2.2. Benchmark results
  • 2.3. Uncertainty about the solution
  • 2.4. Bibliographical references
• 3. Modeling A
  • 3.1. Characteristics of modeling
  • 3.2. Characteristics of the mesh
  • 3.3. Tested sizes and results
• 4. B modeling
  • 4.1. Characteristics of modeling
  • 4.2. Characteristics of the mesh
  • 4.3. Tested sizes and results
• 5. C modeling
  • 5.1. Characteristics of modeling
  • 5.2. Characteristics of the mesh
  • 5.3. Tested sizes and results
• 6. D modeling
  • 6.1. Characteristics of modeling
  • 6.2. Characteristics of the mesh
  • 6.3. Tested sizes and results
• 7. E modeling
  • 7.1. Characteristics of modeling
  • 7.2. Characteristics of the mesh
  • 7.3. Tested sizes and results
• 8. Summary of results