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


Geometry
---------


.. image:: images/10000200000003550000011B7F5AF3F301FBC860.png
    :width: 6.889in
    :height: 2.2835in


.. _RefImage_10000200000003550000011B7F5AF3F301FBC860.png:

Model A, representing the flexure mode of a floor taking into account heavy equipment, is modelled.


Model properties
--------------------

The floor has the following properties:


* mass :math:`{m}_{1}\mathrm{=}1`,


* vertical stiffness :math:`{k}_{1}\mathrm{=}4000`,


* amortization :math:`{\xi }_{1}\mathrm{=}0.07`.

The natural frequency of the floor is :math:`{f}_{1}^{\mathrm{\ast }}\mathrm{=}10.07`.

The equipment has the following properties:


* mass :math:`{m}_{2\mathrm{-}1}\mathrm{=}0.05` :math:`{m}_{2\mathrm{-}2}\mathrm{=}0.025` :math:`{m}_{2\mathrm{-}3}\mathrm{=}0.025`,


* vertical stiffness :math:`{k}_{2\mathrm{-}1}\mathrm{=}200` :math:`{k}_{2\mathrm{-}2}\mathrm{=}800` :math:`{k}_{2\mathrm{-}3}\mathrm{=}50`,


* amortization :math:`{\xi }_{2}\mathrm{=}0.05`.

The natural frequencies of each equipment are: :math:`{f}_{2\mathrm{-}1}\mathrm{=}10.07`, :math:`{f}_{2\mathrm{-}2}\mathrm{=}28.47` and :math:`{f}_{2\mathrm{-}3}\mathrm{=}7.12`.

In the case studied, the mass ratio is :math:`\lambda \mathrm{=}\frac{{m}_{2}}{{m}_{1}}\mathrm{=}0.1`. Since the frequency of an equipment is identical to that of the support, we are in a case where the interaction is maximum.


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

Boundary conditions: Node N1 is blocked.

Loading: a sinusoidal acceleration is imposed on the mass-spring system :math:`f(t)=\mathrm{sin}(2\mathrm{\pi }20t)`

The transient response of the system is calculated with the operator DYNA_VIBRA on a physical basis (BASE_CALCUL =' PHYS ') in transient (TYPE_CALCUL =' TRAN'), with a time step of 0.1 ms.