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


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

Models POU_D_E and DIS_TR

 Number of knots: 19

 Number of stitches: 19 i.e. 18 SEG2 and 1 POI1

Node group:

:math:`\mathrm{PALIER}\text{\_}A`

:math:`\mathrm{PALIER}\text{\_}B`


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


* **First modal calculation: it is of type GEP** **.We solve it*via* the operator CALC_MODES + SOLVEUR_MODAL =_F (METHODE =' SORENSEN ') (concept MODES).


.. csv-table::

    ":math:`N°` "," :math:`\mathrm{FREQ}(\mathrm{Hz})`
    displayed in the .mess", "Tolerance"
    "2", "124.231", "10-6"
    "3", "124.231", "10-6"
    "4", "498.302", "10-6"
    "5", "498.302", "10-6"
    "6", "1118.15", "10-6"
    "7", "1118.15", "10-6"
    "8", "1993.47", "10-6"
    "9", "1993.47", "10-6"
    "10", "2021.39", "10-6"
    "11", "2850.72", "10-6"



* 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{RAYON\_CONTOUR}}}{2\pi }` (if APM). We specify the counting method used (Sturm or APM).


.. csv-table::

    "Concept", "FREQ_MIN/
    CENTRE_CONTOUR "," FREQ_MAX/
    RAYON_CONTOUR "," NB_FREQ ", "Counting method"
    "NBMOD01 ", "-1.0", "120.0", "1
    We count :math:`{\lambda }_{1}`. ", "Sturm"
    "NBMOD02 ", "-1.0", "130.0", "3
    We count :math:`{({\lambda }_{i})}_{\text{i=1,3}}`. ", "Sturm"
    "NBMOD03 ", "-1.0", "1200.0", "7
    We count :math:`{({\lambda }_{i})}_{\text{i=1,7}}`. ", "Sturm"
    "NBMOD11 ", "0.0+0.0j", "5.684 105"
    (= :math:`{(\mathrm{120x2}\pi )}^{2}`)", "1
    Same NBMOD01 "," APM"
    "NBMOD12 ", "0.0+0.0j", "6.671 105"
    (= :math:`{(\mathrm{130x2}\pi )}^{2}`)", "3
    Same NBMOD02 "," APM"
    "NBMOD13 ", "0.0+0.0j", "5.684 107"
    (= :math:`{(\mathrm{1200x2}\pi )}^{2}`)", "7
    Same NBMOD03 "," APM"



* **Second modal calculation:** it is of type QEP *\*.**It is solved*via* using the CALC_MODES + SOLVEUR_MODAL =_F (METHODE ='QZ') operator (='QZ') (concept MODEQ).


.. csv-table::

    ":math:`N°` [1] _", ":math:`\mathrm{FREQ}(\mathrm{Hz})`
    displayed in .mess
    (= :math:`\frac{\mathrm{\Im }({\lambda }_{i})}{2\pi }`)", ":math:`\mathit{AMORTISSEMENT}`
    displayed in .mess
    (= :math:`\frac{\mathrm{-}\mathrm{\Re }({\lambda }_{i})}{\mathrm{\mid }{\lambda }_{i}\mathrm{\mid }}`)", "Eigenvalue module
    (= :math:`\mathrm{\mid }{\lambda }_{i}\mathrm{\mid }`)", "Tolerance"
    "Not applicable", "Not included in *Code_Aster* because true eigenvalue", "Not applicable", "0", "Not applicable"
    "Not applicable", "Not included in *Code_Aster* because true eigenvalue", "Not applicable", "0", "Not applicable"
    "1", "123.915
    + the conjugate complex", "10-11", "778.5", "0.5"
    "2", "124.546
    + the conjugate complex", "10-09", "782.5", "0.5"
    " ... "," ... "," ... "," ... ", "..."
    "10", "2850.72
    + the conjugate complex", "10-15", "18849.5", "0.5"
    "11", "3099.17
    + the conjugate complex", "10-11", "19472.6", "0.5"
    " ... "," ... "," ... "," ... ", "..."
    "41", "21273.2
    + the conjugate complex", "10-12", "133663.4", "0.5"
    "42", "21380.2
    + the conjugate complex", "10-12", "134335.7", "0.5"
    " ... "," ... "," ... "," ... ", "..."



* We are also testing the INFO_MODE command. Since it is a QEP with real matrices, its eigenvalues are either real or complex conjugate. So we can only use the APM method here. It determines the number of eigenvalues (NB_FREQ) contained here strictly in the disk with center CENTRE_CONTOUR and radius RAYON_CONTOUR.


.. csv-table::

    "Concept", "CENTRE_CONTOUR "," RAYON_CONTOUR "," "," NB_FREQ ", "Enumeration method"
    "NBMOD04 ", "0.0+0.0j", "779.114
    (= :math:`\mathrm{124x2}\pi`)", "4
    We count the 2 zero values + the :math:`({\lambda }_{\mathrm{1,}}\stackrel{ˉ}{{\lambda }_{1}})` couple. "," APM"
    "NBMOD05 ", "0.0+779.114j
    (= :math:`0.0+\mathrm{124x2}\pi j`)", "7", "2
    We count the 2 values :math:`{\lambda }_{1}` and :math:`{\lambda }_{2}` without their conjugate. "," APM"
    "NBMOD06 ", "0.0+0.0j", "1.884 104"
    (= :math:`\mathrm{3000x2}\pi`)", "22
    We count the 2 zero values + the :math:`{({\lambda }_{i},\stackrel{ˉ}{{\lambda }_{i}})}_{\text{i=1,10}}` couples. "," APM"
    "NBMOD07 ", "0.0+0.0j", "1.338 105"
    (= :math:`\mathrm{21300x2}\pi`)", "84
    We count the 2 zero values + the :math:`{({\lambda }_{i},\stackrel{ˉ}{{\lambda }_{i}})}_{\text{i=1,41}}` couples. "," APM"
    "NBMOD08 ", "779.114 (1.0+j)
    (= :math:`\mathrm{124x2}\pi (1.0+j)`)", "701.203
    (= :math:`\mathrm{0.9x}\mathrm{124x2}\pi`)", "0"," APM"



.. [1] Only the order in the Code_Aster data structure, since there is no order relationship in the complex plane.