1. Reference problem

1.1. Geometry

1.2. Material properties

\(E\mathrm{=}98\mathrm{696,044}\mathit{MPa}\)

\(\nu \mathrm{=}0\)

\(\rho \mathrm{=}{3.10}^{6}\mathit{kg}\mathrm{/}{m}^{3}\)

Rayleigh proportional damping: \(C\mathrm{=}\lambda K+\mu M\), \(\lambda \mathrm{=}5.{10}^{\mathrm{-}4}\), \(\mu \mathrm{=}5\)

1.3. Boundary conditions and loads

Imposed displacement at the end \(C\): \(u(C)\mathrm{=}\stackrel{ˉ}{u}f(t)\) with \(\stackrel{ˉ}{u}\mathrm{=}{10}^{\mathrm{-}3}m\) and \(f(t)\) evolution as a function of Heaviside time: \(f(t)\mathrm{=}1\), \(t\mathrm{\ge }0\).

\(A\) recessed end

1.4. Initial conditions

Zero initial displacement at all points.

Initial speed zero at all points.