1. Reference problem#

1.1. Geometry#

_images/Object_1.svg

1.2. Material properties#

Link stiffness: \(k\mathrm{=}{28.10}^{3}{\mathit{N.m}}^{\mathrm{-}1}\)

2 cases:

  • \({k}_{1}=k/10\), \({k}_{2}=\mathrm{10k}\)

  • \({k}_{1}=\mathrm{10k}\), \({k}_{2}=k/10\)

Point mass: \(m=10\mathrm{kg}\)

Unidirectional viscous damping: \(c\mathrm{=}50{\mathit{kg.s}}^{\mathrm{-}1}\)

1.3. Boundary conditions and loads#

\(A\) recessed end.

Force applied at the \(B\) end: \(F(t)={F}_{0}\alpha (t)\) with \(\{\begin{array}{}\alpha (t)=1\text{si}0\le t\le 1s\\ \alpha (t)=0\text{sinon}\end{array}\)

and \({F}_{0}\mathrm{=}\mathrm{5N}\).

1.4. Initial conditions#

The system is at rest at \(t=0\): \(u(0)=0\) and \(\frac{\mathrm{du}}{\mathrm{dt}}(0)=0\)