1. Reference problem#

1.1. Geometry#

The structure is composed of a full rotor of length \(L\) with a constant circular cross section with a disk located at a third of its length.

_images/100002000000020E00000120659BD39C6FB9B062.png

Modeling:

Mass (\(\mathit{kg}\))

\({I}_{\mathit{zz}}\) (\({\mathit{kg.m}}^{2}\))

\({I}_{\mathit{xx}}\mathrm{=}{I}_{\mathit{yy}}\) (\({\mathit{kg.m}}^{2}\))

Disk

16.47

0.1861

0.09427

Table 1.1-1 : Disc characteristics

Beam length:

\(L=0.4m\)

Circular section:

Diameter: \(D=0.02m\)

1.2. Material properties#

\(E\mathrm{=}{2.10}^{11}\mathit{Pa}\)

\(\nu =0.3\)

\(\rho \mathrm{=}7800\mathit{kg}\mathrm{/}{m}^{3}\)

1.3. Boundary conditions#

The rotor is supported by two infinitely rigid bearings at both ends and on an elastic bearing with viscous damping at two-thirds of its length. The tier coefficients are as follows:

\({K}_{\mathit{xx}}={2.10}^{5}{\mathit{N.m}}^{-1}\); \({K}_{\mathit{yy}}={5.10}^{5}{\mathit{N.m}}^{-1}\); \({K}_{\mathit{xy}}={K}_{\mathit{yx}}=\mathrm{0 }\)

\({C}_{\mathit{xx}}={4.10}^{1}N/({\mathit{m.s}}^{-1})\); \({C}_{\mathit{yy}}\mathrm{=}{1.10}^{2}N\mathrm{/}({\mathit{m.s}}^{\mathrm{-}1})\); \({C}_{\mathit{xy}}={C}_{\mathit{yx}}=0\)