Table 1 List of parameters.
Parameters | Definition | Parameters | Definition |
|---|---|---|---|
\(M_{\text {ud1}}\) | Unbalance mass of disk 1 | \(M_{\text {d2}}\) | Mass of disk 2 |
\(M_{\text {ud2}}\) | Unbalance mass of disk 2 | v(x, t) | Displacement in the z-axis |
I | Moment of inertia of shaft | w(x, t) | Displacement in the y-axis |
\(I_{21}\) | Diametrical mass moment of inertia of disk 1 | \(K_h\) | Radial stiffnesses of the stator |
\(I_{22}\) | Diametrical mass moment of inertia of disk 2 | \(K_l\) | Linear stiffnesses of the bearings |
\(I_{11}\) | Polar mass moment of inertia of disk 1 | \(K_{nl}\) | Nonlinear stiffnesses of the bearings |
\(I_{12}\) | Polar mass moment of inertia of disk 2 | \(C_b\) | Damping of the bearings |
\(\dot{\beta }\) | Shaft rotational speed | \(C_r\) | Damping of the shaft |
\(r_1\) | Eccentricity of the disk 1 unbalance | \(\rho\) | Mass density of shaft |
\(r_2\) | Eccentricity of the disk 2 unbalance | A | Shaft cross-sectional area |
\(M_{\text {d1}}\) | Mass of disk 1 | E | Young’s modulus of elasticity of the shaft |
