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


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

The model consists of Timoshenko's straight beam elements: POU_D_T.

Divided into 199 elements uniformly distributed throughout the tube:


.. csv-table::

    "Section :math:`[\mathrm{AB}]`:", "99 elements"
    "Section :math:`[\mathrm{BC}]`:", "1 element"
    "Section :math:`[\mathrm{CD}]`:", "99 elements"


Nodes :math:`A` and :math:`D` are blocked in the following directions:


.. csv-table::

    ":math:`X`, :math:`Y` and :math:`Z` in translation"
    ":math:`Y` in rotation"



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

The total number of nodes used for this mesh is 200.

The meshes (type SEG2) are 199 in number.

The mesh file is in ASTER format.


Calculation steps
----------------

The fluid flow velocity profile and the parameters taking into account fluid-structure coupling are defined by operators DEFI_FONC_FLUI and DEFI_FLUI_STRU.

We then calculate the modal parameters of our structure taking into account fluid-elastic forces with CALC_FLUI_SRU.

The definition of the multiple excitation zones is carried out by a call to the operator DEFI_SPEC_TURB, which makes it possible to establish the link between interspectral matrix and shape functions. The excitations are then projected onto the modal basis using the operator PROJ_SPEC_BASE and the modal response interspectra are calculated by the operator DYNA_SPEC_MODAL.

Finally, the autospectra of constraints at the nodes are deduced by a call to REST_SPEC_PHYS.

We can only calculate the spectral response for one flow speed at a time, so these last three steps (PROJ_SPEC_BASE, DYNA_SPEC_MODAL, REST_SPEC_PHYS) are carried out in a loop, in the command file, where we go through the list of flow velocities.


Tested values
---------------


.. csv-table::

    "**Identification**", "**Reference**
    **1 area**", "**Calculation**
    **2 excitement areas**", "**%**
    **difference**"
    "**Frequency** Mode 2
    Fluid—elastic coupling (speed :math:`\mathrm{1,5}m/s`)
    Uniform speed profile (:math:`1m/s`)
    Viscache coefficients 1", "32.28018 Hz", "32.28018 Hz", "0.0"
    "**Reduced dampening** Mode 2
    Fluid—elastic coupling (speed :math:`\mathrm{1,5}m/s`)
    Uniform speed profile (:math:`1m/s`)
    Viscache coefficients 1", "8.960594E—01%", "8.960594E—01%", "0.0"
    "**Frequency** Mode 2
    Fluid—elastic coupling (speed :math:`\mathrm{1,5}m/s`)
    Stair speed profile (:math:`\mathrm{0,5}` and :math:`1m/s`)
    Viscache coefficients 1", "31.39222 Hz", "31.39222 Hz", "0.0"
    "**Reduced dampening** Mode 2
    Fluid—elastic coupling (speed :math:`\mathrm{1,5}m/s`)
    Stair speed profile (:math:`\mathrm{0,5}` and :math:`1m/s`)
    Viscache coefficients 1", "9,170868E—01%", "9,170842E—01%", "0.0"
    "**Frequency** Mode 2
    Fluid—elastic coupling (speed :math:`\mathrm{1,5}m/s`)
    Stair speed profile (:math:`\mathrm{0,5}` and :math:`1m/s`)
    Uniform Coefficient", "32.19244 Hz", "32.19244 Hz", "0.0"
    "**Reduced dampening** Mode 2
    Fluid—elastic coupling (speed :math:`\mathrm{1,5}m/s`)
    Stair speed profile (:math:`\mathrm{0,5}` and :math:`1m/s`)
    Uniform Coefficient", "5.947656E—0.1%", "5.947633E—0.1%", "0.0"
    "**Frequency** Mode 2
    Fluid—elastic coupling (speed :math:`\mathrm{1,5}m/s`)
    Uniform speed profile (:math:`\mathrm{0,5}m/s`)
    Uniform Coefficient", "32.28018 Hz", "32.28018 Hz", "0.0"
    "**Reduced dampening** Mode 2
    Fluid—elastic coupling (speed :math:`\mathrm{1,5}m/s`)
    Uniform speed profile (:math:`\mathrm{0,5}m/s`)
    Uniform Coefficient", "6.071243E—01%", "6.071211E—01%", "0.0"
    "Value of the **RMS of movement**
    for flow speed :math:`\mathrm{0,7}m/s`
    Uniform speed profile (:math:`\mathrm{0,5}m/s`)
    Uniform Coefficient", "1.20960E—06 m", "1.20960E—06 m", "1.20953E—06 m", "—0.005"
    "Value of the **RMS of movement**
    for flow speed :math:`\mathrm{1,1}m/s`
    Uniform speed profile (:math:`\mathrm{0,5}m/s`)
    Uniform Coefficient", "8.46330E—06 m", "8.46290E—06 m", "—0.005"
    "Value of the **RMS of movement**
    for flow speed :math:`\mathrm{1,5}m/s`
    Uniform speed profile (:math:`\mathrm{0,5}m/s`)
    Uniform Coefficient", "3.91328E—05 m", "3.91308E—05 m", "—0.005"
    "Value of the **RMS of movement**
    for flow speed :math:`\mathrm{0,7}m/s`
    Uniform speed profile (:math:`\mathrm{1,0}m/s`)
    Viscache coefficients 1", "2.83236E—06 m", "2.83221E—06 m", "—0.005"
    "Value of the **RMS of movement**
    for flow speed :math:`\mathrm{1,1}m/s`
    Uniform speed profile (:math:`\mathrm{1,0}m/s`)
    Viscache coefficients 1", "1.36880E—05 m", "1.36783E—05 m", "—0.005"
    "Value of the **RMS of movement**
    for flow speed :math:`\mathrm{1,5}m/s`
    Uniform speed profile (:math:`\mathrm{1,0}m/s`)
    Viscache coefficients 1", "3.24409E—05 m", "3.24393E—05 m", "—0.005"