.. _V2.02.141:

**v2.02.141** SDLL141 - Natural frequencies of a single beam, subject to the gyroscopic effect.
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**Summary:**

This problem consists in looking for the vibration frequencies of a beam supported at each of its ends, on infinitely rigid supports. The beam is solid, has a circular cross section and is subject to a constant speed of rotation. It does not have any discs.

Five models are studied:


* Modeling A: the beam is along axis :math:`x`,


* B modeling: the beam is along the :math:`t` axis such as :math:`t` direction vector of the bisector :math:`(x,y)`.


* C modeling: the beam is along the :math:`t` axis such as :math:`t` direction vector of the bisector, and the :math:`(x,y)` mass is distributed by discrete elements installed on each of the nodes.


* D modeling: the beam is along the :math:`x` axis. The cross section is circular and variable with the two radii :math:`\mathrm{R1}` and :math:`\mathrm{R2}` the same.


* E modeling: resumes C modeling with declaration of the characteristics of the discrete elements in the local coordinate system.

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 duplication of modes. The evolution of natural frequencies as a function of the speed of rotation makes it possible to build the Campbell diagram.

The references are based on the Euler-Bernouilli theory.

The results obtained are in good agreement with those given in reference.


.. toctree::
    :hidden:

    self

.. toctree::
    :maxdepth: 2
    :numbered:

    Probl_me_de_r_f_rence
    Solution_de_r_f_rence
    Mod_lisation_A
    Mod_lisation_B
    Mod_lisation_C
    Mod_lisation_D
    Mod_lisation_E
    Synth_se_des_r_sultats