3. Modeling A#

3.1. Characteristics of modeling#

The springs and point masses are modelled by discrete elements with 3 degrees of freedom DIS_T. Nodes \(N2\) and \(N3\) are slightly offset according to \(Y\), \(Y=\mathrm{0,01}m\) and \(Y=-\mathrm{0,01}m\) respectively, which does not change the results as only the problem according to \(X\) is solved.

_images/100002010000017D000000D21A3CFE6296669D24.png

Node \(N1\) is embedded and subjected to an imposed acceleration \(\gamma (t)\).

The mode of the first spring mass system is first calculated by imposing \({u}_{x}({P}_{3})=0\). Then the mode of the second, by imposing \({u}_{x}({P}_{2})=0\). A single modal base is created from these two modes, using the DEFI_BASE_MODALE command with the NUME_REF option. A dynamic calculation is then performed with the command DYNA_NON_LINE using modal damping deduced from these modes.

3.2. Characteristics of the mesh#

Number of knots: 3

Number of meshes and types: 2 DIS_T

3.3. Tested sizes and results#

The solutions tested are the relative displacement in \(t=10s\):

Node

Reference

Tolerance

\(N2\) (dot \({P}_{2}\))

0.538736

1%

\(N3\) (dot \({P}_{3}\))

0.538736

1%