1. Reference problem

1.1. Geometry

1.2. Material properties

Link stiffness: \({k}_{1}=4.{10}^{9}{\mathrm{N.m}}^{-1}\), \({k}_{2}=5.33{10}^{8}{\mathrm{N.m}}^{-1}\)

Point masses: \({m}_{1}={10}^{6}\mathrm{kg}\), \({m}_{2}={m}_{3}={12.10}^{6}\mathrm{kg}\)

Unidirectional viscous damping: \({C}_{1}=1.2566{10}^{6}{\mathrm{kg.s}}^{-1}\), \({C}_{2}=9.0478{10}^{6}{\mathrm{kg.s}}^{-1}\)

1.3. Boundary conditions and loads

Completely free system.

Loading at point \({P}_{3}\) along the \(x\) axis: \(F(t)0={F}_{0}\mathrm{sin}(\Omega t)\) for \(t\ge 0\) with \({F}_{0}={5.10}^{4}N\) and \(\Omega =19\pi {\mathrm{rad.s}}^{-1}\).

1.4. Initial conditions

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