2. Benchmark solution

2.1. Calculation method used for the reference solution

The reference solutions are the one presented in the book by Michel LALANNE and Guy FERRARIS and the one obtained with the code CADYRO, finite element software intended to predict the dynamic behavior of rotors.

Numerical results CADYRO were obtained with Timoshenko type beam elements. The modeling is carried out with 4 nodes (3 beam elements).

2.2. Reference quantities and results

With an unbalanced loading, the values tested are the amplitude maximas for the node corresponding to the disk, for two laws of increase in rotation speed ranging from 0 to \(5000\mathit{tr}\mathrm{/}\mathit{min}\) (concept of resonance at the critical speed).

Modeling A also tests methods for accessing generalized coordinate values (displacements, speeds and accelerations) from a transitory calculation result on a generalized basis, i.e. the methods getDisplacementValues, getVelocityValues, and getAccelerationValues. At the end of the transitory calculation, the extraction of the values of generalized coordinates is tested indirectly, via the comparison of coordinates on a physical basis (displacements, speeds and accelerations) obtained from the operator « REST_GENE_PHYS » and those obtained from a physical database retrieval entirely carried out in Python, using the access methods mentioned above.

The correct functioning of the methods for defining generalized coordinate values, namely methods setDisplacementValues, setVelocityValues, and setAccelerationValues, are also being tested.

2.3. Uncertainty about the solution

Less than 5%.

2.4. Bibliographical references

• Michel LALANNE and Guy FERRARIS, Rotordynamics, Prediction in Engineering, JOHN WILEY AND SONS (1990).

• CADYRO, finite element software designed to predict the dynamic behavior of rotors under bending.