1. Reference problem#

1.1. Geometry#

The length of the beam is equal to: \(L=1m\)

The section of the beam is full circular with radius: \(R=0.1m\)

The gap between the beam and the elastic support is equal to: \(J={10}^{-4}m\)

\(E={10}^{10}\mathit{Pa}\)

\(\nu =0.3\)

\(\mathrm{\rho }={10}^{6}\mathit{kg}/{m}^{3}\)

The stiffness of the contact spring is equal to: \({K}_{c}={10}^{8}N/m\)

On the whole structure: \(\mathrm{DX}=\mathrm{DZ}=\mathrm{DRY}=\mathrm{DRX}=0\).

At point \(A\): \(\mathrm{DY}=\mathrm{DRZ}=0\).

At the free end of the beam: from instant \(t=0s\), \(\mathrm{Fy}=–1000.N\)

Structure initially at rest.