1. Reference problem#

1.1. Geometry#

The structure is composed of a rotor with a length L2 and a circular section, two infinitely rigid bearings and a mass of girders with circular sections.

Figure 1.1-a -a: Rotor model with 2 bearings and one massive

Coordinates of the nodes in coordinate system \((X,Y,Z)\):

Support: \(A(0.0/-0.25/0.0)\)

\(B(0.0/-0.25/1.0)\)

Rotor: \(C(0.0/0.0/1.0)\)

1.2. Material properties#

The geometric and material characteristics are listed in the following table.

Material		\(E=2{10}^{11}N/{m}^{2}\)	\(\rho =7800\mathrm{kg}/{m}^{3}\)	\(\nu =0.0\)
Rotor length	\(L=2m\)
Rotor radius	\(\mathrm{Rr}=0.1m\)
Length of the massif	\(L=2m\)
Width of the massif	\(l=0.5m\)
Height of the massif	\(H=1m\)
Radius of the beams of the massif	\(\mathrm{Rm}=0.1m\)

Table 1.2-1

The two level nodes are located exactly in the middle of each side of the massif.

The translational stiffness coefficients of the bearings are: \(\mathrm{Kzz}=\mathrm{Kyy}=1.0E+12{\mathrm{kg.s}}^{-2}\)

\(\mathrm{Kzy}=\mathrm{Kyz}=0.0\mathrm{kg.s}-2\)

\(\mathrm{Czz}=\mathrm{Cyy}=\mathrm{Czy}=\mathrm{Cyz}=0.0{\mathrm{kg.s}}^{-1}\)

1.3. Boundary conditions#

The rotor bearings rest on the mass by means of connections that are considered to be infinitely rigid. The four legs of the massif are embedded. The rotor and the massif are therefore perfectly coupled to the bearing nodes, according to the CRAIG - BAMPTON method.