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

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

This modeling seeks to be similar to the document [:ref:`2 <2>`] from 2010. For this, the calculated mass matrix is full.

Modal analysis identifies the first 14 modes and five spectral analyses are carried out:


1. Combination SRSS


2. Combination CQC


3. Combination CQC with static correction


4. Gupta-like combination with :math:`\mathit{f1}\mathrm{=}\mathrm{2,80}\mathit{Hz}` and :math:`\mathit{f2}\mathrm{=}\mathrm{11,90}\mathit{Hz}` with static correction


5. Gupta-like combination with :math:`\mathit{f1}\mathrm{=}\mathrm{2,80}\mathit{Hz}` and :math:`\mathit{f2}\mathrm{=}\mathrm{6Hz}` with static correction


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

The quantities tested are the natural frequencies of the first 14 modes and the reactions to the supports of the structure. The tests use values from ANSYS as references. They are backed by non-regression tests with a tolerance of :math:`\mathrm{1,E-6}`.

.. csv-table::

    "**Clean Fashion**", "**Reference**
    **Frequencies (Hz)**", "**Tolerance**
    **Aster_Code (%)**"
    "**1**", "2.91", "1"
    "**2**", "4.44", "2"
    "**3**", "4.86", "1"
    "**4**", "5.02", "1"
    "**5**", "6.95", "1"
    "**6**", "7.58", "2"
    "**7**", "7.82", "1"
    "**8**", "10.94", "2"
    "**9**", "11.65", "3"
    "**10**", "11.78", "2"
    "**11**", "12.8", "2"
    "**12**", "14.32", "3"
    "**13**", "15.17", "8"
    "**14**", "15.79", "6"



.. csv-table::

    "**Knots**", "**Efforts**", "**Reference calculation 1**
    **(F:lbs, m:lbs-inch)**", "**Tolerance**
    **Aster_code**
    **calculation 1 (%)**", "**Reference calculation 2**"
    **(F:lbs, m:lbs-inch)**", "**Tolerance**
    **Aster_code**
    **calculation 2 (%)**", "**Reference calculation 3**
    **(F:lbs, m:lbs-inch)**", "**Tolerance**
    **Aster_code**
    **calculation 3 (%)**"
    "**1**", ":math:`\mathit{FX}` ", "30.69", "30.69", "13", "30.81", "13", "43.85", "3"
    "**1**", ":math:`\mathit{FY}` ", "15.34", "15.34", "10", "10", "12.59", "9", "15.21", "8"
    "**1**", ":math:`\mathit{FZ}` ", "49.04", "49.04", "9", "9", "24.91", "5"
    "**1**", ":math:`\mathit{MX}` ", "1515.03", "1515.03", "6", "6", "764.29", "7", "766.72", "7"
    "**1**", ":math:`\mathit{MY}` ", "1219.62", "1219.62", "6", "6", "932.32", "0.15", "934.03", "1"
    "**1**", ":math:`\mathit{MZ}` ", "1100.66", "1100.66", "12", "1096.58", "12", "1108.78", "11"
    "**4**", ":math:`\mathit{FX}` ", "45.19", "45.19", "5", "45.02", "5", "77.36", "3"
    "**4**", ":math:`\mathit{FZ}` ", "82.15", "82.15", "2", "55.61", "56.12", "1"
    "**7**", ":math:`\mathit{FY}` ", "27.87", "27.87", "2", "15.78", "11", "15.99", "9"
    "**11**", ":math:`\mathit{FY}` ", "21.54", "21.54", "20", "20", "19.59", "20", "20"
    "**11**", ":math:`\mathit{FZ}` ", "42.91", "42.91", "4", "42.35", "2", "43.43", "3"
    "**15**", ":math:`\mathit{FX}` ", "368.83", "368.83", "2", "388.99", "3", "389.64", "3"
    "**17**", ":math:`\mathit{FY}` ", "44.28", "4.28", "0.3", "45.83", "2", "45.95", "2"
    "**17**", ":math:`\mathit{FZ}` ", "53.12", "53.12", "2", "55.06", "1", "55.31", "0.1"
    "**36**", ":math:`\mathit{FY}` ", "162.84", "162.84", "3", "169.14", "1", "171.57", "3"
    "**36**", ":math:`\mathit{FZ}` ", "80.96", "80.96", "8", "81.34", "6", "90.69", "10"
    "**38**", ":math:`\mathit{FX}` ", "116.92", "116.92", "4", "135.99", "5", "566.65", "12"
    "**38**", ":math:`\mathit{FY}` ", "52.46", "52.46", "2", "54.26", "1", "54.29", "1"
    "**38**", ":math:`\mathit{FZ}` ", "39.12", "39.12", "7", "7", "4.55", "6", "50.45", "5.5"
    "**38**", ":math:`\mathit{MX}` ", "2543.44", "2543.44", "1", "2606.69", "3", "2606.69", "3"
    "**38**", ":math:`\mathit{MY}` ", "2533.41", "2533.41", "65", "2894.27", "5", "3142.75", "4.5"
    "**38**", ":math:`\mathit{MZ}` ", "3650.45", "3650.45", "2", "3763.01", "1", "3764.97", "1"
    "**23**", ":math:`\mathit{FX}` ", "177.23", "177.23", "5", "177.23", "5", "245.05", "4"
    "**23**", ":math:`\mathit{FY}` ", "145.37", "145.37", "4", "151.53", "1", "151.99", "1"
    "**31**", ":math:`\mathit{FX}` ", "9.41", "9.41", "2", "11.09", "2", "54.42", "6"
    "**31**", ":math:`\mathit{FY}` ", "22.08", "22.08", "6", "6", "24.77", "5", "27.73", "4"
    "**31**", ":math:`\mathit{FZ}` ", "31.36", "31.36", "8", "32.11", "7", "32.26", "7"
    "**31**", ":math:`\mathit{MX}` ", "1971.58", "1971.58", "16", "2068", "14", "2072.03", "14"
    "**31**", ":math:`\mathit{MY}` ", "267.63", "267.63", "23", "304.18", "23", "567.6", "28"
    "**31**", ":math:`\mathit{MZ}` ", "603.06", "603.06", "6", "706.86", "3", "1912.58", "4"



.. csv-table::

    "**Knots**", "**Efforts**", "**Reference calculation 4**"
    **(F:lbs, m:lbs-inch)**", "**Tolerance**
    **calculation 4 (%)**", "**Reference calculation 5**
    **(F:lbs, m:lbs-inch)**", "**Tolerance**
    **calculation 5 (%)**"
    "**1**", ":math:`\mathit{FX}` ", "54.42", "54.42", "1", "52.05", "1"
    "**1**", ":math:`\mathit{FY}` ", "3.43", "3.43", "8", "2.73", "16"
    "**1**", ":math:`\mathit{FZ}` ", "6.61", "6.61", "4", "4.93", "25"
    "**1**", ":math:`\mathit{MX}` ", "190.18", "190.18", "13", "135.39", "11"
    "**1**", ":math:`\mathit{MY}` ", "858.44", "858.44", "2", "877.81", "4"
    "**1**", ":math:`\mathit{MZ}` ", "966.87", "966.87", "3", "864.96", "2"
    "**4**", ":math:`\mathit{FX}` ", "105.14", "105.14", "1", "114.06", "1"
    "**4**", ":math:`\mathit{FZ}` ", "42.48", "42.48", "6", "34.9", "6"
    "**7**", ":math:`\mathit{FY}` ", "8.77", "8.77", "8.77", "8.77", "39"
    "**11**", ":math:`\mathit{FY}` ", "16.71", "16.71", "33", "12.44", "37"
    "**11**", ":math:`\mathit{FZ}` ", "49.19", "49.19", "2", "61.99", "3"
    "**15**", ":math:`\mathit{FX}` ", "547.38", "547.38", "2", "641.84", "1"
    "**17**", ":math:`\mathit{FY}` ", "35.92", "35.92", "1", "26.39", "2"
    "**17**", ":math:`\mathit{FZ}` ", "56.34", "56.34", "2", "46.86", "3"
    "**36**", ":math:`\mathit{FY}` ", "81.01", "81.01", "5", "61.16", "21"
    "**36**", ":math:`\mathit{FZ}` ", "60.87", "60.87", "3", "42.38", "20"
    "**38**", ":math:`\mathit{FX}` ", "750.45", "750.45", "10", "739.29", "10"
    "**38**", ":math:`\mathit{FY}` ", "46.02", "46.02", "2", "42.92", "1"
    "**38**", ":math:`\mathit{FZ}` ", "45.53", "45.53", "8", "41.67", "6.5"
    "**38**", ":math:`\mathit{MX}` ", "914.22", "914.22", "9", "369.64", "3"
    "**38**", ":math:`\mathit{MY}` ", "3191.39", "3191.39", "7", "2909.01", "6"
    "**38**", ":math:`\mathit{MZ}` ", "3248.59", "3248.59", "2", "3036.62", "1"
    "**23**", ":math:`\mathit{FX}` ", "347.2", "347.2", "4", "304.8", "5"
    "**23**", ":math:`\mathit{FY}` ", "49.61", "49.61", "11", "16.75", "12"
    "**31**", ":math:`\mathit{FX}` ", "63.82", "63.82", "3", "61.95", "3"
    "**31**", ":math:`\mathit{FY}` ", "16.89", "16.89", "4", "13.34", "6"
    "**31**", ":math:`\mathit{FZ}` ", "19.53", "19.53", "11", "12.96", "4.2"
    "**31**", ":math:`\mathit{MX}` ", "1235.04", "1235.04", "19", "695.41", "19"
    "**31**", ":math:`\mathit{MY}` ", "818.08", "818.08", "31", "757.2", "32"
    "**31**", ":math:`\mathit{MZ}` ", "2460.9", "2460.9", "2", "2319.49", "3"