# OS-V: 0420 Free Thin Square Plate

Test No. FV12 A thin square plate model that contains three rigid body modes. OptiStruct investigates the repeated eigenvalues and kinematically incomplete suppressions of the thin plate in Normal Modes Analysis.

## Model Files

## Benchmark Model

The 4-node quad elements with 8x8 mesh configuration are used to model the plate. The x-translation, y-translation displacements and z-rotational displacements are fixed for all nodes.

**Property****Value**- E
- 200 x 10
^{9}N/m^{2} - $\upsilon $
- 0.3
- $\rho $
- 8000 kg/m
^{3}

## Modal Analysis Results

`f*`

- Closed form solution

S# | Mode # | OptiStruct Results | F* (Hz) | Normalized Value |
---|---|---|---|---|

1 | Mode 4 | 1.619 | 1.622 | 0.9981 |

2 | Mode 5 | 2.394 | 2.360 | 1.0144 |

3 | Mode 6 | 2.9896 | 2.922 | 1.0231 |

4 | Mode 7 and 8 | 4.2315 | 4.233 | 0.9996 |

5 | Mode 9 | 7.8002 | 7.416 | 1.0518 |

6 | Mode 10 (HOE) | 7.8848 | 7.392 | 1.0667 |

Mode 4 | Mode 5 | Mode 6 | |||
---|---|---|---|---|---|

`f*` CQUAD4 |
1.622 Hz 0.9964 |
`f*` CQUAD4 |
2.360 Hz 1.0145 |
`f*` CQUAD4 |
2.922 Hz 1.0231 |

Modes 7 and 8 | Mode 9 | Mode 10 | |||
---|---|---|---|---|---|

`f*` CQUAD4 |
4.233 Hz 0.9978 |
`f*` CQUAD4 |
7.416 Hz 1.0496 |
F[HOE] CQUAD4 |
7.392 Hz 1.1746 |

## Reference

NAFEMS R0015 - Selected benchmarks for natural frequency analysis