2. Benchmark solution

2.1. Calculation method used for the reference solution

The reference solution is the one presented in the book by Michel LALANNE and Guy FERRARIS.

The numerical results were obtained using a finite element code, with Timoshenko beam elements. The modeling is carried out with 14 nodes (13 beam elements).

2.2. Benchmark results

• 10 first frequencies specific to stopping (\(\Omega =0\)).

• 10 first frequencies specific to a rotation speed of \(\Omega =25000\mathrm{tr}/\mathrm{min}\).

• With an unbalanced loading, values of the 7 amplitude maximas for the points \(A\), \(C\) and \(E\), for a rotation speed varying from \(0\) to \(30000\mathrm{tr}/\mathrm{min}\).

2.3. Uncertainty about the solution

Less than 1%.

2.4. Bibliographical references

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