1. Reference problem

1.1. Geometry

The system is composed of a mass, a spring and a shock absorber. It admits a single degree of freedom in translation.

1.2. Material properties

Link stiffness: \(k\mathrm{=}{25.10}^{3}{\mathit{N.m}}^{\mathrm{-}1}\)

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

Viscous damping:

\(c\mathrm{=}{c}_{\mathit{critique}}\); \(c\mathrm{=}\mathrm{0,01}{c}_{\mathit{critique}}\); \(c\mathrm{=}{10}^{\mathrm{-}5}{c}_{\mathit{critique}}\)

with \({c}_{\mathit{critique}}\mathrm{=}1000{\mathit{kg.s}}^{\mathrm{-}1}\)

1.3. Boundary conditions and loads

Recessed A end

Harmonic force following x at the resonance frequency at point \(B\):

\(F(t)\mathrm{=}{F}_{0}\mathrm{sin}(\omega t)\) for \(t\mathrm{\ge }0\) with \({F}_{0}\mathrm{=}5N\) and \(\omega \mathrm{=}\sqrt{\frac{k}{m}}\mathrm{=}50{\mathit{rad.s}}^{\mathrm{-}1}\).

1.4. Initial conditions

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