Modélisation C
==============


Caractéristiques de la modélisation
-----------------------------------

Éléments discrets de rigidité, amortissement et masse.


.. image:: images/Object_14.svg
    :width: 440
    :height: 159


.. _RefImage_Object_14.svg:

Caractéristiques des éléments :


.. csv-table::

    "DISCRET:", "masse nodale", "M_T_D_N"
    "", "rigidité linéaire", "K_T_D_L"
    "", "amortissement linéaire", "A_T_D_L(:math:`c={10}^{-5}{c}_{\mathrm{critique}}` )"


Conditions aux limites : au nœud :math:`\mathrm{N1}` DDL_IMPO DX = DY = DZ = 0.

Noms des nœuds : :math:`{P}_{1}=\mathrm{N1}` , :math:`{P}_{2}=\mathrm{N2}` .

Méthodes de calcul :


*   Intégration sur la base modale avec Newmark (:math:`\alpha =0,25` , :math:`\delta =0,5` )

Pas de temps :math:`\Delta t={10}^{-\mathrm{3s}}`


*   Intégration sur la base modale avec Euler

Pas de temps :math:`\Delta t={10}^{-\mathrm{3s}}`

Durée d’observation : :math:`5s` .


Caractéristiques du maillage
----------------------------

Nombre de nœuds : 2

Nombre de mailles et type : 1 maille SEG2


Grandeurs testées et résultats
------------------------------


*   Déplacement du point B


.. csv-table::

    "", "**Déplacement**", "**Déplacement**", "", "**Déplacement**", ""
    "**Temps**", "**Référence**", "**NEWMARK**", "**Tolérance**", "**EULER**", "**Tolérance**"
    "(:math:`s` )", "(:math:`m` )", "**Aster** (:math:`m` )", "(%)", "**Aster** (:math:`m` )", "(%)"
    "0,06", "3,11105 E–4", "3,10936 E–4", "0.5 %", "3,11181 E–4", "0.5 %"
    "0,13", "–6,13250 E–4", "–6,13016 E–4", "0.5 %", "–6,13380 E–4", "0.5 %"
    "0,25", "–1,25380 E–3", "–1,25304 E–3", "0.5 %", "–1,25418 E–3", "0.5 %"
    "0,69", "3,44945 E–3", "3,44691 E–3", "0.5 %", "3,45069 E–3", "0.5 %"
    "1,01", "–4,88729 E–3", "–4,89081 E–3", "0.5 %", "–4,88547 E–3", "0.5 %"
    "2,32", "1,12876 E–2", "1,12475 E–2", "0.5 %", "1,13069 E–2", "0.5 %"
    "3,64", "–1,77960 E–2", "–1,77100 E–2", "0.5 %", "–1,78360 E–2", "0.5 %"
    "4,96", "2,43613 E–2", "2,42198 E–2", "0.5 %", "2,44242 E–2", "0.5 %"



*   Vitesse du point B


.. csv-table::

    "", "**Vitesse**", "**Vitesse**", "", "**Vitesse**", ""
    "**Temps**", "**Référence**", "**NEWMARK**", "**Tolérance**", "**EULER**", "**Tolérance**"
    "(:math:`s` )", "(:math:`{\mathrm{m.s}}^{-1}` )", "**Aster** (:math:`{\mathrm{m.s}}^{-1}` )", "(%)", "**Aster** (:math:`{\mathrm{m.s}}^{-1}` )", "(%)"
    "0,04", "9,09284 E–3", "9,08897 E–3", "0.5 %", "9,08230 E–3", "0.5 %"
    "0,10", "–2,39724 E–2", "–2,39637 E–2", "0.5 %", "–2,40269 E–2", "0.5 %"
    "0,22", "–5,49964 E–2", "–5,49680 E–2", "0.5 %", "–5,48752 E–2", "0.5 %"
    "0,66", "1,64958 E–1", "1,64879 E–1", "0.5 %", "1,64882 E–1", "0.5 %"
    "1,04", "2,56456 E–1", "2,56547 E–1", "0.5 %", "2,57280 E–1", "0.5 %"
    "2,36", "–5,79010 E–1", "–5,80019 E–1", "0.5 %", "–5,81033 E–1", "0.5 %"
    "3,68", "8,97631 E–1", "9,00729 E–1", "0.5 %", "9,00668 E–1", "0.5 %"
    "5,00", "–1,21164", "–1,21829", "0.5 %", "–1,21531", "0.5 %"



Remarques
---------

Les résultats sont testés au niveau des pics où les valeurs sont les plus significatives.

Dans l’intervalle d’observation, on reste très en dessous du régime permanent en résonance dont l’amplitude de déplacement est :math:`10m` .