Modeling A
==============


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

Discrete translational stiffness element DIS_T


.. 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_T_D_N", "in absolute coordinate system", ":math:`(m\mathrm{=}10.)`"
    "all-mesh stiffness matrices", "K_T_D_L", "in local coordinate system", ":math:`(\mathit{Kx}\mathrm{=}1.{10}^{5})`"
    "at the end nodes", "K_T_D_N", "in local coordinate system", ":math:`({K}_{x}\mathrm{=}1.{10}^{5})`"


Boundary conditions:

DDL_IMPO: (TOUT: 'OUI' DZ: 0.)

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

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

.. math::
: label: EQ-None

    \ mathit {Point} A\ mathrm {=}\ mathit {N1}


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**"
    "Translation 1
    (:math:`\mathit{Dy}`)
    :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"
    "Translation 8
    (:math:`\mathit{Dy}`)
    :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**"
    "Translation 1
    (:math:`\mathit{Dy}`)
    :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"
    "Translation 8
    (:math:`\mathit{Dy}`)
    :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**"
    "Translation 1
    (:math:`\mathit{Dy}`)
    :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"
    "Translation 8
    (:math:`\mathit{Dy}`)
    :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%.

We are also testing the INFO_MODE command. Since GEP is standard (real symmetric matrices) its eigenvalues belong only to the real axis. In this case, we can therefore compare the two counting methods (COMPTAGE/METHODE =' STURM 'and' APM ') and check that they actually give the same results.

We thus determine the number of eigenvalues (NB_FREQ) contained strictly in a frequency band [FREQ_MIN, FREQ_MAX] (if Sturm) or in the disk with center FREQ_CENTRE and radius, in frequency, :math:`\frac{\sqrt{\text{FREQ\_RAYON\_CONTOUR}}}{2\pi }` (if APM). We specify the counting method used (Sturm or APM).


.. csv-table::

    "Concept", "FREQ_MIN/
    FREQ_CENTRE "," FREQ_MAX/
    FREQ_RAYON_
    CONTOUR "," NB_FREQ ", "Counting method"
    "NBMOD01 ", "0.0", "5", "5", "0", "Sturm"
    "NBMOD02 ", "0.0", "21", "4
    We count :math:`{({\lambda }_{i})}_{\text{i=1,4}}` ", "Sturm"
    "NBMOD03 ", "0.0", "32", "8
    We count :math:`{({\lambda }_{i})}_{\text{i=1,8}}` ", "Sturm"
    "NBMOD11 ", "0.0+0.0j", "986.96
    (= :math:`{(5\mathrm{\times }2\pi )}^{2}`)", "0
    Same NBMOD01 "," APM"
    "NBMOD12 ", "0.0+0.0j", "1740.99
    (= :math:`{(21\mathrm{\times }2\pi )}^{2}`)", "4
    Same NBMOD02 "," APM"
    "NBMOD13 ", "0.0+0.0j", "4042.58"
    (= :math:`{(32\mathrm{\times }2\pi )}^{2}`)", "8
    Same NBMOD03 "," APM"
    "NBMOD4 "," :math:`10000.0+\mathrm{0.0j}`
    (= :math:`{(\mathrm{15.91x2}\pi )}^{2}`)", "5000.0", "1
    We count :math:`{\lambda }_{1}` "," APM"
    "NBMOD5 "," :math:`1000.0(10.0+j)` ", "900.0", "0"," APM"



notes
---------

Calculations made by:


.. code-block:: text

    CALC_MODES

    OPTION =' AJUSTE ',
CALC_FREQ =_F (FREQ =( 5., 10., 10., 15., 15., 15., 15., 15., 20., 24., 24., 27., 30., 32.)),
SOLVEUR_MODAL =_F (OPTION_INV =' DIRECT ')

**Contents of the results file:**

8 first natural frequencies, eigenvectors and modal parameters