B modeling
==============


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

Compared to modeling A, only the density values are modified, which are multiplied by 30:


* Fluid: :math:`\rho \mathrm{=}30000{\mathit{kg.m}}^{\mathrm{-}3}` (water),


* Structure: :math:`{\rho }_{s}\mathrm{=}23400\mathit{kg}\mathrm{/}{m}^{3}` (steel).

This is done in such a way as to reduce the cutoff frequency of the problem.


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

The aim is to test the spectral response of the structure to turbulent excitation previously defined in modeling A but calculated for 128 frequency points. For various frequencies, we test the value of the spectral response at node 2 of the board which is located :math:`13.75m` from the center of the board.

The theoretical answer was evaluated with Python.


.. csv-table::

    "**Identification**", "**frequency (** :math:`\mathrm{Hz}` **)**", "**Reference type**", "**Reference**", "**%** tolerance"
    ":math:`\mathit{SF1F1}(\omega )\omega \mathrm{=}0.01` ", "1.59155e-03", "'ANALYTIQUE'", "7.288480E8", "0.2"
    ":math:`\mathit{SF}1F1(\mathrm{\omega })\mathrm{\omega }=1` ", "1.59155e-01", "'ANALYTIQUE'", "7.532370E6", "0.8"



.. csv-table::

    "**Identification**", "**frequency (** :math:`\mathit{Hz}` **)**", "**Reference type**", "**Reference**", "**%** tolerance"
    ":math:`{S}_{U}(\mathrm{\omega })f=0.08275` ", "8.27500e-02", "'NON_REGRESSION'", "-", "-"
    ":math:`{S}_{U}(\mathrm{\omega })f=0.05` ", "5.00000e-02", "'NON_REGRESSION'", "-", "-"
    ":math:`{S}_{U}(\mathrm{\omega })f=0.025` ", "2.50000e-02", "'NON_REGRESSION'", "-", "-"