v2.06.102 SHLL102 — Harmonic response of a beam with 3 disks, subject to the gyroscopic effect.

Summary:

This problem consists in validating the effect of the gyroscopic matrix on a beam supported at each of its ends, on linear supports, on a harmonic calculation with a loading of the unbalance type. The beam is solid, has a circular cross section and has three disks.

For this test case, the unbalance type load is installed on disk 2. The comparison relates to the value of the resonance peaks of the movements of the disk 2.

This problem therefore makes it possible to test the effect of the gyroscopic matrix that was developed for a straight beam. The gyroscopic effect leads to the modification of the resonance frequencies and the amplitude of movements.

The results obtained are in good agreement with those given in reference. 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. Loading
• 4. Results
• 5. Summary of results