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


Geometry
---------

An anti-seismic device is placed between two jaws (rectangles shaded in the following figure) which are themselves placed on a vibrating table subjected to an acceleration imposed in the direction X. It is modelled by a non-linearity of the "anti-seismic device" type placed on either side of a mass-spring system.


.. image:: images/Object_1.svg
    :width: 303
    :height: 274


.. _RefImage_Object_1.svg:


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

The jaws that insert the device are each modelled by a mass-spring system:

connection stiffness: :math:`k={10}^{10}N/m`;

point mass: :math:`m=25\mathrm{kg}`.

The device tested is an anti-seismic device of type JARRET. Its characteristics are as follows:


* :math:`\mathrm{K1}=6.{10}^{6}N/m` (RIGI_K1),


* :math:`\mathrm{K2}=\mathrm{0,53}{10}^{6}N/m` (RIGI_K2),


* :math:`\mathrm{Py}=1200` (SEUIL_FX),


* :math:`C=\mathrm{0,07}{10}^{5}` (C),


* :math:`\mathrm{alpha}=\mathrm{0,2}` (PUIS_ALPHA),


* :math:`\mathrm{xmax}=\mathrm{0,03}m` (DX_MAX).


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

**Boundary conditions**

The only authorized movements are translations according to axis :math:`X`. Points :math:`C` and :math:`D` are embedded: :math:`\mathrm{dx}=\mathrm{dy}=\mathrm{dz}=0`. The other points are free to translate according to :math:`\mathrm{dx}`: :math:`\mathrm{dy}=\mathrm{dz}=0`.

**Loading**

Point :math:`D` is subject to transverse acceleration in the direction :math:`x` :math:`{\gamma }_{1}(t)\mathrm{=}\mathrm{0,66}\mathrm{sin}(\omega t)m\mathrm{/}{s}^{2}` with :math:`\omega \mathrm{=}2\pi`, point :math:`C` is fixed.


Initial conditions
--------------------

At the initial moment, the device is at rest: at :math:`t=0`, :math:`\mathrm{dx}(0)=0`, :math:`\mathrm{dx}/\mathrm{dt}(0)=0` at all points.