1. Reference problem#
1.1. Geometry#
A rotor model supported by 2 bearings (nodes \(\mathrm{B1}\) and \(\mathrm{B2}\) in the figure below), whose stiffness and damping matrices are non-symmetric. It is composed of 2 discs and 3 shaft sections.
Image 1.1-1: Rotor model with 2 discs and 2 asymmetric bearings
1.2. Material properties#
The geometric and material characteristics are listed in the following table.
Material |
\(E={2.10}^{11}N/{m}^{2}\) |
\(\rho =7800\mathrm{kg}/{m}^{3}\) |
\(\nu =0.3\) |
|
Disc |
\(\mathrm{D1}\) |
\(M=3.5\mathrm{kg}\) |
\({I}_{D}=3.5{10}^{-3}\mathrm{kg}{m}^{2}\) |
\({I}_{P}={7.10}^{-3}\mathrm{kg}{m}^{2}\) |
\(\mathrm{D2}\) |
\(M=3.0\mathrm{kg}\) |
\({I}_{D}=3.0{10}^{-3}\mathrm{kg}{m}^{2}\) |
\({I}_{P}={6.10}^{-3}\mathrm{kg}{m}^{2}\) |
|
Table 1.2-1 : Geometric characteristics and material
The characteristics of the bearings are indicated in the following table.
Level |
\(\mathrm{P1}\) |
|
|
\({K}_{\mathrm{xz}}=-{1.10}^{7}N/m\) |
|
||
\({C}_{\mathrm{xx}}=8.{10}^{3}\mathrm{Ns}/m\) |
|
||
\({C}_{\mathrm{xz}}=-3.{10}^{3}\mathrm{Ns}/m\) |
|
||
Level |
\(\mathrm{P2}\) |
|
|
\({K}_{\mathrm{xz}}=-2.{10}^{6}N/m\) |
|
||
\({C}_{\mathrm{xx}}=6.{10}^{3}\mathrm{Ns}/m\) |
|
||
\({C}_{\mathrm{xz}}=-1.5{10}^{3}\mathrm{Ns}/m\) |
|
Table 1.2-2: Characteristics of bearings
1.3. Boundary conditions and loads#
To block rigid body movements in the \(y\) direction, we block the degrees of freedom \(\mathrm{DY}\) and \(\mathrm{DRY}\) at the level node \(\mathrm{B1}\).
Charging is a harmonic force at a constant speed of rotation.