# OS-V: 1030 Rigid Jeffcott Model

This problem describes the Rigid Jeffcott model for rotor dynamics.

## Model Files

Before you begin, copy the file(s) used in this problem
to your working directory.

## Benchmark Model

The model details are as follows:

- Unbalanced rigid disc on a massless rigid shaft.
- CELAS, CTETRA4 and RBE2 elements defined.
- ASYNC Complex Eigenvalue Analysis with Gyroscopic effects.
- Rotor speed increments via RSPEED from 0 to 100 Hz, in steps of 10 Hz.

## Material

The MAT1 material properties are:

**Property****Value**- Young's modulus (E)
- 1.0E+20 ton/s
^{2}-mm - Poisson's Ratio (NU)
- 0.3
- Mass Density (RHO)
- 1.0 ton/mm
^{3}

## Results

The reference results are obtained by:

$$s\text{\hspace{0.17em}}=\text{\hspace{0.17em}}\sigma \text{\hspace{0.17em}}+\text{\hspace{0.17em}}i\omega $$

Where, $$\left\{\begin{array}{l}\omega \text{\hspace{0.17em}}=\text{\hspace{0.17em}}\frac{{J}_{p}\Omega \text{\hspace{0.33em}}\pm \text{\hspace{0.33em}}\sqrt{{J}_{p}^{2}{\Omega}^{2}\text{\hspace{0.33em}}+\text{\hspace{0.33em}}4{J}_{t}{K}_{22}}}{2{J}_{t}}\\ \sigma \text{\hspace{0.33em}}=\text{\hspace{0.33em}}0\end{array}\right.$$

- ${J}_{p}$
- Inertia moment of polar axis.
- ${J}_{t}$
- Inertia moment of transverse axis.
- ${K}_{22}$
- Stiffness of the transverse rotation.
- $\Omega $
- Spinning speed [rad/s].
- $\omega $
- Whirling frequency [rad/s].

RotorSpeed (Hz) | OptiStruct_mode 1* | OptiStruct_mode 2** | Reference_mode 1^{1} |
Reference_mode 2^{1} |
---|---|---|---|---|

0 | 246 | 245 | 245.7213 | 245.7213 |

10 | 255 | 236 | 255.254 | 236.5446 |

20 | 265 | 227 | 265.1419 | 227.7231 |

30 | 275 | 219 | 275.3828 | 219.2546 |

40 | 286 | 211 | 285.9728 | 211.1353 |

50 | 297 | 203 | 296.9069 | 203.3599 |

60 | 308 | 196 | 308.1784 | 195.9211 |

70 | 319 | 189 | 319.7799 | 188.8141 |

80 | 331 | 182 | 331.7025 | 182.0274 |

90 | 344 | 175 | 343.9369 | 175.5524 |

100 | 356 | 169 | 356.4728 | 169.3789 |

* mode 1 - Forward Whirl Mode

** mode 2 - Backward Whirl Mode

^{1}Genta, Giancarlo. “Dynamics of Rotating Systems.” Mechanical Engineering Series, 2005, doi:10.1007/0-387-28687-x.