1. Reference problem#

1.1. Geometry#

_images/1000020000000355000000A93F4BAE99F84FCD49.png

Beam length: \(L=1m\)

Section:

Inner radius \(=0.09m\)

Outer radius \(=0.10m\)

1.2. Material properties#

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

\(\nu =0.3\)

\(\rho ={1.10}^{4}\mathrm{kg}/{m}^{3}\)

Modeling A: no amortization

Modeling B: Proportional Damping (RAYLEIGH):

\(C=\alpha K+\beta M\) with \(\alpha =6.5{10}^{-6}s\) and \(\beta =16.0{s}^{-1}\).

These values correspond to a depreciation reduced by 1% in the first mode of the structure.

1.3. Boundary conditions and loads#

On the whole structure we impose \(\mathrm{DY}=\mathrm{DZ}=\mathrm{DRX}=\mathrm{DRY}=\mathrm{DRZ}=0\).

In point \(A\) we impose the embedding condition \(\mathrm{DX}=0\).

In \(\mathrm{N10}\) we apply a constant force starting from the instant \(t=0\): \({F}_{x}=–100N\).

_images/100002000000032E0000014844B5093A8C46BF22.png

1.4. Initial conditions#

The structure is initially at rest.