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


Geometry
---------

We calculate the response of a linear system composed of three masses and three springs to an acceleration imposed at its anchor point :math:`(A)`:


.. image:: images/1000108E00001CBB0000077142BB037A4805ADE5.svg
    :width: 370
    :height: 96


.. _RefImage_1000108E00001CBB0000077142BB037A4805ADE5.svg:


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


* connection stiffness: :math:`k={k}_{1}={k}_{2}={k}_{3}=1000N/m`;


* point masses: :math:`m={m}_{1}={m}_{2}={m}_{3}=1\mathrm{kg}`.


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

**Boundary conditions**

The only authorized movements are translations according to axis :math:`x`.

Point :math:`A` is embedded: :math:`\mathrm{dx}=\mathrm{dy}=\mathrm{dz}=\mathrm{drx}=\mathrm{dry}=\mathrm{drz}=0`.

**Loading**

Anchor point :math:`A` is subject to acceleration, an increasing function of time, in the direction :math:`x`: :math:`\gamma (t)\mathrm{=}2\mathrm{.}{10}^{5}\mathrm{.}{t}^{2}` (:math:`t` varies from :math:`0` to :math:`\mathrm{0,1}s`).


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

The system is initially at rest: at :math:`t=0`, :math:`\mathrm{dx}(0)=0`, and :math:`\mathrm{dx}/\mathrm{dt}(0)=0` at all points.