1. Reference problem#

1.1. Geometry#

_images/10000200000003550000011B7F5AF3F301FBC860.png

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

1.2. Model properties#

The floor has the following properties:

  • mass \({m}_{1}\mathrm{=}1\),

  • vertical stiffness \({k}_{1}\mathrm{=}4000\),

  • amortization \({\xi }_{1}\mathrm{=}0.07\).

The natural frequency of the floor is \({f}_{1}^{\mathrm{\ast }}\mathrm{=}10.07\).

The equipment has the following properties:

  • mass \({m}_{2\mathrm{-}1}\mathrm{=}0.05\) \({m}_{2\mathrm{-}2}\mathrm{=}0.025\) \({m}_{2\mathrm{-}3}\mathrm{=}0.025\),

  • vertical stiffness \({k}_{2\mathrm{-}1}\mathrm{=}200\) \({k}_{2\mathrm{-}2}\mathrm{=}800\) \({k}_{2\mathrm{-}3}\mathrm{=}50\),

  • amortization \({\xi }_{2}\mathrm{=}0.05\).

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

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

1.3. Boundary conditions and loads#

Boundary conditions: Node N1 is blocked.

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

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.