1. Reference problem

1.1. Geometry

The system in question consists of a simple heavy mass placed on a rigid support subjected to an imposed seismic, sinusoidal vibration. Contact, as well as dry friction, are modelled by penalization. The system therefore has two degrees of translational freedom (horizontal and vertical).

A spring of very low stiffness connects the mass to the support in all three directions. This spring is a calculation device, intended to avoid the nullity of the frequency associated with the rigid mode of horizontal translation of the mass. The*Aster* results taking into account the presence of this spring are little different from the results that would be obtained without spring.

1.2. Model properties

Spring stiffness (in all three directions):	\(k\mathrm{=}{3.10}^{\mathrm{-}5}N\mathrm{/}m\)
mass:	\(m\mathrm{=}1\mathit{kg}\)
gravity:	\(g\mathrm{=}10m\mathrm{/}{s}^{2}\)
Coulomb coefficient:	\(\mu \mathrm{=}\mathrm{0,1}\)

1.3. Boundary conditions, initial conditions and loads

The mass rests on the rigid plane at dimension \(z\mathrm{=}0\).

The harmonic acceleration imposed at the base has equation \(a\mathrm{=}{a}_{0}\mathrm{sin}(\omega t)\) as equation. In particular, it is zero at the initial moment. The movement of the support satisfies the equation

, and so begins its movement to the left, with the initial speed not zero

.

The initial move (to

) of the mass is taken to be zero. The mass is considered to be in a state of adhesion at the initial instant. It therefore has the same non-zero speed as the support at

.

The calculations are carried out for various values of the maximum acceleration:

m/s

,

m/s

,

m/s

and

m/s

and a pulsation value: \(\omega \mathrm{=}2\pi\).