.. _V2.03.109:

**v2.03.109** SDLS109 - Natural frequencies of a thick cylindrical ring
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**Summary:**

This test is inspired by a vibratory study carried out on collector VVP of N4 slices. This collector is thick and has a maximum thickness to mean radius ratio of 0.13. This value, which may be typical of an industrial structure, is slightly higher than the validity limit value usually recognized for plates and shells. In this study, the modeling of the collector in shells is then evaluated by comparison with a volume model on a ring.

This test makes it possible to evaluate the eigenvalue search operator CALC_MODES [:ref:`U4.52.02 <U4.52.02>`] with the stiffness and mass matrices corresponding to the following models:


1. plates of type DKQ (finite element MEDKQU4) and DSQ (finite element MEDSQU4),


2. plates of type DKT (finite element MEDKTR3) and DST (finite element MEDSTR3) with a mesh made of spikes and a mesh of stars,


3. three-dimensional shells of type COQUE_3D (finite elements MEC3QU9H and MEC3TR7H),


4. wire elements with beam kinematics and Fourier modes TUYAU (finite element METUSEG3) and TUYAU_6M (finite element MET6SEG3),


5. COQUE_SOLIDE type solid plate elements

The results obtained are compared with the solution resulting from a volume modeling of the ring (finite element MECA_HEXA8) showing Fourier modes of order 2 (ovalization) and 3 (trifoliate) as well as 2 modes out of plane.


.. toctree::
    :hidden:

    self

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

    Probl_me_de_r_f_rence
    Mod_lisation_de_r_f_rence
    Mod_lisation_A
    Mod_lisation_B
    Mod_lisation_C
    Mod_lisation_D
    Mod_lisation_E
    Mod_lisation_F
    Mod_lisation_H
    Synth_se_des_r_sultats