Benchmark solution
=====================


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).


Benchmark results
----------------------


* 10 first frequencies specific to stopping (:math:`\Omega =0`).


* 10 first frequencies specific to a rotation speed of :math:`\Omega =25000\mathrm{tr}/\mathrm{min}`.


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


Uncertainty about the solution
---------------------------

Less than 1%.


Bibliographical references
---------------------------

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