Reference problem
=====================

Geometry
---------


.. image:: images/100020A2000028B900001D8F07876160CF147A61.svg
    :width: 525
    :height: 381


.. _RefImage_100020A2000028B900001D8F07876160CF147A61.svg:


* pipe outer diameter: :math:`0.185m`


* pipe thickness: :math:`6.12m`


* radius of curvature of the elbows: :math:`0.922m`


Material properties
-----------------------

.. csv-table::

    ":math:`E=1.658E+11\mathrm{Pa}` "," :math:`\nu =0.3` "," :math:`\rho =13404.106\mathrm{kg}/{m}^{3}` (pipe full of water)"



Boundary conditions and loads
-------------------------------------

Points 1 and 15 embedded (:math:`u=v=w={\theta }_{x}={\theta }_{y}={\theta }_{z}=0`).

Loading: not applicable for modal analysis.

For spectral analysis: definition of an acceleration spectrum at the supports for a damping of :math:`\text{2\%}`.

.. csv-table::

    "Frequency (:math:`\mathrm{Hz}`)", "1", "10", "10", "30", "100", "10000"
    "Acceleration (:math:`g`)
    following :math:`x` and :math:`y` ", "0.2", "2. ", "2. ", "0.2", "0.2"
    "Acceleration (:math:`g`)
    following z", "0.1", "1. ", "1. ", "0.1", "0.1"