# 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

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

## 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.

The material properties are:

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

## Modal Analysis Results

The frequency of each targeted mode is normalized with the closed form solution. The closed form
solution is not available for mode 10, use target value for H.O.E. instead.

`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