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


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

The modeling is in POU_D_E beams, plus an element of discrete stiffness DIS_T, without mass.


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

Number of knots: 82

Number of meshes and types: 81 SEG2.


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

    Natural frequencies
~~~~~~~~~~~~~~~~~~~~~~~~


.. csv-table::

    "**Mode**", "**Reference value (** :math:`\mathit{Hz}` **)**"
    "1", "1.5491943226358"
    "2", "3.107551438801"
    "3", "9.3245300415725"
    "4", "9.5870612490701"
    "5", "15.547112609525"
    "6", "21.778952588689"
    "7", "26.36518615935"
    "8", "28.023559687023"
    "9", "34.284194672867"
    "10", "40.56369329853"
    "11", "46.864148730311"
    "12", "50.060463212131"
    "13", "53.18629486166"
    "14", "59.528203850076"


**Table** 3.3.1-1 **: Natural frequencies**


3.3.2 Single-support spectral analysis
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Calculation method


.. csv-table::

    "Modal base with the 14 previous modes (:math:`<60\mathit{Hz}`)"
    "Damping reduced by 0.07 for all modes"
    "Taking into account the static contribution of neglected natural modes"
    "Combination of dynamic modal responses using the Gupta method (frequency_1: :math:`14.6\mathit{Hz}`, frequency_2: :math:`40\mathit{Hz}`)
    COMB_MODE =_F (TYPE =' GUPTA ')"
    "Quadratic combination of directional responses
    COMB_DIRECTION =_F (TYPE =' QUAD ')"


**Table 3.3.2-** 1 **: Calculation method**

Displacements: DEPL (m)


+---------+---------+---------------------+
|Bow      |Component|Reference (:math:`m`)|
+---------+---------+---------------------+
|:math:`H`|DX       |3.2396432663129E-03  |
+         +---------+---------------------+
|         |DY       |0.0E+00              |
+         +---------+---------------------+
|         |DZ       |1.3091056936155E-03  |
+         +---------+---------------------+
|         |DRX      |0.0E+00              |
+         +---------+---------------------+
|         |DRY      |1.4915675244137E-04  |
+         +---------+---------------------+
|         |DRZ      |0.0E+00              |
+---------+---------+---------------------+
|:math:`R`|DX       |9.4449003235868E-08  |
+         +---------+---------------------+
|         |DY       |0.0E+00              |
+         +---------+---------------------+
|         |DZ       |1.5182762043245E-07  |
+         +---------+---------------------+
|         |DRX      |0.0E+00              |
+         +---------+---------------------+
|         |DRY      |0.0E+00              |
+         +---------+---------------------+
|         |DRZ      |0.0E+00              |
+---------+---------+---------------------+
|:math:`S`|DX       |9.056974877545E-06   |
+         +---------+---------------------+
|         |DY       |0.0E+00              |
+         +---------+---------------------+
|         |DZ       |7.2126964195151E-06  |
+         +---------+---------------------+
|         |DRX      |0.0E+00              |
+         +---------+---------------------+
|         |DRY      |1.6632972701712E-06  |
+         +---------+---------------------+
|         |DRZ      |0.0E+00              |
+---------+---------+---------------------+
|:math:`O`|DX       |0.0E+00              |
+         +---------+---------------------+
|         |DY       |0.0E+00              |
+         +---------+---------------------+
|         |DZ       |0.0E+00              |
+---------+---------+---------------------+

**Table 3.3.2-** 2 **: travel**

Absolute accelerations: ACCE_ABSOLU (:math:`{\mathit{N.m}}^{\mathrm{-}2}`)


+---------+---------+------------------------------------------------+
|Bow      |Component|Reference (:math:`{\mathit{N.m}}^{\mathrm{-}2}`)|
+---------+---------+------------------------------------------------+
|:math:`H`|DX       |0.61824985176146                                |
+         +---------+------------------------------------------------+
|         |DY       |0.25000000000000                                |
+         +---------+------------------------------------------------+
|         |DZ       |0.56926959473828                                |
+         +---------+------------------------------------------------+
|         |DRX      |0.0E+00                                         |
+         +---------+------------------------------------------------+
|         |DRY      |0.0936304357433140                              |
+         +---------+------------------------------------------------+
|         |DRZ      |0.0E+00                                         |
+---------+---------+------------------------------------------------+
|:math:`R`|DX       |0.24879675464209                                |
+         +---------+------------------------------------------------+
|         |DY       |0.25000000000000                                |
+         +---------+------------------------------------------------+
|         |DZ       |0.24941080125292                                |
+         +---------+------------------------------------------------+
|         |DRX      |0.0E+00                                         |
+         +---------+------------------------------------------------+
|         |DRY      |0.0E+00                                         |
+         +---------+------------------------------------------------+
|         |DRZ      |0.0E+00                                         |
+---------+---------+------------------------------------------------+
|:math:`S`|DX       |0.20128061437786                                |
+         +---------+------------------------------------------------+
|         |DY       |0.25000000000000                                |
+         +---------+------------------------------------------------+
|         |DZ       |0.22473145378803                                |
+         +---------+------------------------------------------------+
|         |DRX      |0.0E+00                                         |
+         +---------+------------------------------------------------+
|         |DRY      |0.011827974442827                               |
+         +---------+------------------------------------------------+
|         |DRZ      |0.0E+00                                         |
+---------+---------+------------------------------------------------+
|:math:`O`|DX       |0.25000000000000                                |
+         +---------+------------------------------------------------+
|         |DY       |0.25000000000000                                |
+         +---------+------------------------------------------------+
|         |DZ       |0.25000000000000                                |
+---------+---------+------------------------------------------------+

**Table 3.3.2-** 3 **: absolute accelerations**

Nodal reactions: REAC_NODA (:math:`N`)


+---------+---------+---------------------+
|Bow      |Component|Reference (:math:`N`)|
+---------+---------+---------------------+
|:math:`H`|DX       |3.32338062257E-04    |
+         +---------+---------------------+
|         |DY       |9326.6031903447      |
+         +---------+---------------------+
|         |DZ       |9.6944351594654E-08  |
+         +---------+---------------------+
|         |DRX      |7.7721693252872E+02  |
+         +---------+---------------------+
|         |DRY      |8.6738098496576E-05  |
+         +---------+---------------------+
|         |DRZ      |0.0E+00              |
+---------+---------+---------------------+
|:math:`R`|DX       |6.0472578414485E-05  |
+         +---------+---------------------+
|         |DY       |9.3266031903447E+03  |
+         +---------+---------------------+
|         |DZ       |2.6406108097108E-08  |
+         +---------+---------------------+
|         |DRX      |7.7721693252872E+02  |
+         +---------+---------------------+
|         |DRY      |1.9606618500589E+07  |
+         +---------+---------------------+
|         |DRZ      |0.0E+00              |
+---------+---------+---------------------+
|:math:`S`|DX       |2.8288137175073E-03  |
+         +---------+---------------------+
|         |DY       |1.8653206380689E+04  |
+         +---------+---------------------+
|         |DZ       |7.390788273137E-07   |
+         +---------+---------------------+
|         |DRX      |0.0E+00              |
+         +---------+---------------------+
|         |DRY      |0.0E+00              |
+         +---------+---------------------+
|         |DRZ      |0.0E+00              |
+---------+---------+---------------------+
|:math:`O`|DX       |9.4449003235868E+05  |
+         +---------+---------------------+
|         |DY       |0.0E+00              |
+         +---------+---------------------+
|         |DZ       |1.5182762043245E+06  |
+---------+---------+---------------------+

**Table 3.3.2-** 4 **: Nodal reactions**