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


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

Discrete translational stiffness element DIS_T


.. image:: images/10000DF000001FF0000006349EF710CB4B34B431.svg
    :width: 412
    :height: 80


.. _RefImage_10000DF000001FF0000006349EF710CB4B34B431.svg:

Characteristics of the elements


.. csv-table::

    "DISCRET:", "", "", ""
    "with nodal masses", "", "", ""
    "in all nodes", "M_T_D_N", "in absolute coordinate system", ":math:`(m=10.)`"
    "stiffness matrices", "", ""
    "in every mesh", "M_T_D_L", "in absolute coordinate system", ":math:`({K}_{x}={1.10}^{5})`"
    "damping matrices", "", "", "
    "internal meshes", "A_T_D_L", "in absolute coordinate system", ":math:`({C}_{x}=50.)`"
    "initial mesh", "A_T_D_L", "in absolute coordinate system", ":math:`({C}_{x}=250.)`"
    "final mesh", "A_T_D_L", "in absolute coordinate system", ":math:`({C}_{x}=25.)`"


Boundary conditions:


+----------------+------------------------------------------------------+
|DDL_IMPO:       | .. code::                                            |
+                +                                                      +
|                |    ( TOUT:’OUI’ DY: 0. , DZ: 0. )                    |
+----------------+------------------------------------------------------+
|At the end knots| .. code::                                            |
+                +                                                      +
|                |    ( NŒUD: (A B) DX: 0. )                            |
+----------------+------------------------------------------------------+

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


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


.. csv-table::

    "Number of knots:", "10"
    "Number of meshes and types:", "9 SEG2et 8 POI1"



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


.. csv-table::

    "**Frequency**", "**Reference**"
    "Clean mode order 1", "5.53"
    "Clean mode order 2", "10.90"
    "Clean mode order 3", "15.93"
    "Clean mode order 4", "20.45"
    "Clean mode order 5", "24.34"
    "Clean mode order 6", "27.49"
    "Clean mode order 7", "29.84"
    "Clean mode order 8", "31.29"



.. csv-table::

    "**Depreciation**", "**Reference**"
    "Clean mode order 1", "1.521e-2"
    "Clean mode order 2", "2.877e-2"
    "Clean mode order 3", "3.960e-2"
    "Clean mode order 4", "4.709e-2"
    "Clean mode order 5", "5.098e-2"
    "Clean mode order 6", "5.183e-2"
    "Clean mode order 7", "5.115e-2"
    "Clean mode order 8", "5.036e-2"



.. csv-table::

    "**Nature of clean mode**", "**Point**", "**Clean mode Reference in 10** **—3**
    **Real part**
    **Imaginary part**"
    "Translation 1
    (:math:`\mathit{Dy}`)
    :math:`{\mathrm{\Phi }}_{1}` ", "P1
    P2
    P3
    P4
    P5
    P6
    P7
    P8", "4.07, —4.56
    7.97, —8.28
    10.9, —11.0
    12.5, —12.5
    12.5, —12.4
    11.1, —10.9
    8.24, —8.04
    4.41, —4.25"
    "Translation 8
    (:math:`\mathit{Dy}`)
    :math:`{\mathrm{\Phi }}_{8}` ", "P1
    P2
    P3
    P4
    P5
    P6
    P7
    P8", "2.23, —1.14
    —3.71, 2.98
    4.75, —4.41
    —5.25, 5.27
    5.14, —5.43
    —4.44, 4.88
    3.23, —3.69
    —1.66, 2.01"


Eigenmode standardized to the unit modal mass: :math:`{\varphi }_{i}^{t}C{\varphi }_{i}+2{\lambda }_{i}{\varphi }_{i}^{t}M{\varphi }_{i}=1`

:math:`\lambda`: is the eigenvalue associated with damping and natural frequency.


Contents of the results file
----------------------------

The 8 damping and natural frequencies, as well as the associated natural vectors.