D modeling
==============


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

Transposition of the reference test to the case of degrees of freedom of rotation (torsion+inertia spring) using the discrete element of translation/rotation stiffness: DIS_TR.


.. image:: images/10000000000002A0000000DE179A8A60910DB795.png
    :width: 4.8346in
    :height: 1.5417in


.. _RefImage_10000000000002A0000000DE179A8A60910DB795.png:

Characteristics of the elements:


.. csv-table::

    "ORIENTATION:", "in all the nodes", "with an angle :math:`\alpha \mathrm{=}53.130102°`"



.. csv-table::

    "DISCRET:", "", "", ""
    "with nodal masses all nodes", "M_ TR_N ", "in absolute coordinate system", ":math:`({I}_{\mathit{xx}}\mathrm{=}10.)`"
    "all-mesh stiffness matrices", "K_ TR_L ", "in local coordinate system", ":math:`({\mathit{KR}}_{x}\mathrm{=}1.{10}^{5})`"
    "at the knots
    endpoints", "K_ TR_N ", "in local coordinate system", ":math:`({\mathit{KR}}_{x}\mathrm{=}1.{10}^{5})`"


Boundary conditions:

DDL_IMPO: (TOUT: 'OUI' DX: 0., DY: 0., DZ: 0., DRZ: 0.)

LIAISON_DDL: (such as :math:`\mathrm{3DRY}\mathrm{=}\mathrm{4DRY}` in all nodes)

Node names: :math:`{P}_{\mathrm{1,}}{P}_{\mathrm{2,}}\mathrm{....},{P}_{8}`


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

Number of knots: 8

Number of meshes and types: 7 SEG2


Tested sizes and results
------------------------------


.. csv-table::

    "**Identification**
    **Clean mode number**", "**Reference**"
    "1", "5.5274"
    "2", "10.8868"
    "3", "15.9155"
    "4", "20.4606"
    "5", "24.3840"
    "6", "27.5664"
    "7", "29.9113"
    "8", "31.3474"


**Standardized mode with 1 to the largest component**


.. csv-table::

    "**Nature of clean modes**", "**Point**", "**Reference**"
    "Rotation 1
    (:math:`\mathit{DRY}`)
    :math:`{\Phi }_{1}` ", "P1
    P2
    P3
    P4
    P5
    P6
    P7
    P8", "—0.3473
    —0.6527
    —0.8793
    —1.
    —1.
    —0.8793
    —0.6527
    —0.3473"
    "Rotation 8
    (:math:`\mathit{DRY}`)
    :math:`{\Phi }_{8}` ", "P1
    P2
    P3
    P4
    P5
    P6
    P7
    P8", "0.3473
    —0.6527
    0.8793
    —1.
    1.
    —0.8793
    0.6527
    —0.3473"


Maximum error less than: 0.03%.

**Mode standardized to the generalized unit mass**


.. csv-table::

    "**Nature of clean modes**", "**Point**", "**Reference**"
    "Rotation 1
    (:math:`\mathit{DRY}`)
    :math:`{\Phi }_{1}` ", "P1
    P2
    P3
    P4
    P5
    P6
    P7
    P8", "—4.0781E—2
    —7.6654E—2
    —1.0327E—1
    —1.1743E—1
    —1.1743E—1
    —1.0327E—1
    —7.6654E—2
    —4.0781E—2"
    "Rotation 8
    (:math:`\mathit{DRY}`)
    :math:`{\Phi }_{8}` ", "P1
    P2
    P3
    P4
    P5
    P6
    P7
    P8", "4.0781E—2
    —7.6654E—2
    1.0327E—1
    —1.1743E—1
    1.1743E—1
    —1.0327E—1
    7.6654E—2
    —4.0781E—2"


Maximum error less than: 0.03%.

**Standardized mode with unitary generalized stiffness**


.. csv-table::

    "**Nature of clean modes**", "**Point**", "**Reference**"
    "Rotation 1
    (:math:`\mathit{DRY}`)
    :math:`{\Phi }_{1}` ", "P1
    P2
    P3
    P4
    P5
    P6
    P7
    P8", "—1.1742E—3
    —2.2072E—3
    —2.9735E—3
    —3.3813E—3
    —3.3813E—3
    —2 9735E—3
    —2.2072E—3
    —1.1742E—3"
    "Rotation 8
    (:math:`\mathit{DRY}`)
    :math:`{\Phi }_{8}` ", "P1
    P2
    P3
    P4
    P5
    P6
    P7
    P8", "2.0705E—4
    —3.8918E—4
    5.2432E—4
    —5.9621E—4
    5.9621E—4
    —5.2432E—4
    3.8918E—4
    —2.0705E—4"


Maximum error less than: 0.03%.


notes
---------

Calculations made by:


.. code-block:: text

    CALC_MODES

    OPTION =' AJUSTE ',

    CALC_FREQ =_F (FREQ =( 5., 10., 10., 15., 15., 15., 15., 20., 24., 27., 30., 32. )),

    SOLVEUR_MODAL =_F (OPTION_INV =' DIRECT '),

**Contents of the results file:**

8 first natural frequencies, eigenvectors and modal parameters