1. Reference problem#

1.1. 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.

_images/Object_1.svg

1.2. Material properties#

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

connection stiffness: \(k={10}^{10}N/m\);

point mass: \(m=25\mathrm{kg}\).

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

  • \(\mathrm{K1}=6.{10}^{6}N/m\) (RIGI_K1),

  • \(\mathrm{K2}=\mathrm{0,53}{10}^{6}N/m\) (RIGI_K2),

  • \(\mathrm{Py}=1200\) (SEUIL_FX),

  • \(C=\mathrm{0,07}{10}^{5}\) (C),

  • \(\mathrm{alpha}=\mathrm{0,2}\) (PUIS_ALPHA),

  • \(\mathrm{xmax}=\mathrm{0,03}m\) (DX_MAX).

1.3. Boundary conditions and loads#

Boundary conditions

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

Loading

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

1.4. Initial conditions#

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