B modeling
==============


Characteristics of modeling
-----------------------------------

**Modeling**: 18 Equidistributed POU_D_E beam elements


Characteristics of the mesh
----------------------------

The axis of the beam is oriented according to the vector :math:`(\mathrm{cos}(\mathrm{\pi }/4),\mathrm{sin}(\mathrm{\pi }/4)\mathrm{,0})`.


.. csv-table::

    "Mesh:", "Number of nodes: 19"
    "", "Number of meshes and types: 18 SEG2"



.. csv-table::

    "Node names:", "Point :math:`A` = :math:`N1`"
    "", "Point :math:`B` = :math:`N19`"


**3.3** **Tested quantities and results**

Rotor stopped (:math:`\Omega =0`) (frequencies in :math:`\mathrm{Hz}`)


.. csv-table::

    "**Identification**", "**Reference type**", "**Reference value**", "**Tolerance**"
    "Mode 1", "'ANALYTIQUE'", "122.7475"," 0.1%"
    "Mode 2", "'ANALYTIQUE'", "490.9899"," 0.1%"
    "Mode 3", "'ANALYTIQUE'", "1104,7273"," 0.1%"
    "Mode 4", "'ANALYTIQUE'", "1963,9596"," 0.1%"


**Calculation of natural frequencies using the Sorensen algorithm**

Rotating rotor (:math:`\Omega ={10}^{4}{\mathrm{rd.s}}^{-1}`), direct modes (frequencies in :math:`\mathrm{Hz}`)


.. csv-table::

    "**Identification**", "**Reference type**", "**Reference value**", "**Tolerance**"
    "Mode 2", "'ANALYTIQUE'", "125.8150"," 0.1%"
    "Mode 4", "'ANALYTIQUE'", "503,2598"," 0.1%"
    "Mode 6", "'ANALYTIQUE'", "1132,3346"," 0.1%"
    "Fashion 9", "'ANALYTIQUE'", "2013.0393"," 0.1%"


Rotating rotor (:math:`\Omega ={10}^{4}{\mathrm{rd.s}}^{-1}`), retrograde modes (frequencies in :math:`\mathrm{Hz}`)


.. csv-table::

    "**Identification**", "**Reference type**", "**Reference value**", "**Tolerance**"
    "Mode 1", "'ANALYTIQUE'", "119.7548"," 0.1%"
    "Mode 3", "'ANALYTIQUE'", "479.0191"," 0.1%"
    "Mode 5", "'ANALYTIQUE'", "1077,7931"," 0.1%"
    "Mode 7", "'ANALYTIQUE'", "1916.0765"," 0.1%"