# OS-V: 0365 Simply-Supported Thin Square Plate Transient Forced Vibration Response

Test 13T OptiStruct is used to investigate the Peak Displacement in z-direction, the time at the peak displacement, extreme fiber bending stress at undamped Natural Frequency and the Static displacement at the center of the plate.

## Model Files

## Benchmark Model

The 2nd order and 1st order quad elements are used to model the square plate of thickness
0.05 m. The z-rotation and x, y translations are fixed for all the nodes, z-translation is
fixed along all four edges, x-rotation is fixed along the edge x = 0 and x = 10 and
y-rotation is fixed along the edge y = 0 and y = 10. A suddenly applied step load
F_{0} = 100 N/m^{2} is induced in the z-direction. For modal analysis
solution, a damping ratio of 0.02 is applied in all 16 modes at a time step of 0.002 secs
and for direct solution, Rayleigh damping factor α_{1} = 0.299 and α_{2} =
1.339×10^{-3} at a time step of 0.002 secs are given.

**Material Properties****Value**- Young’s Modulus
- 200 × 10
^{9}N/m^{2} - Poisson’s Ratio
- 0.3
- Density
- 8000 kg/m
^{3}

## Frequency Response Summary

`f*`

- Closed form solution

Peak Displacement (mm) | Time at Peak Displacement (sec) | Peak Stress (N/mm^{2}) |
Static Displacement (mm) | |
---|---|---|---|---|

Reference Solution | 3.523 | 0.210 | 2.484 | 1.817 |

HOE: | ||||

Direct Solution | 3.637 | 0.212 | 2.784 | 1.832 |

Normalized | 0.968655485 | 0.990566038 | 0.892241379 | 0.991812227 |

Modal Solution | 3.643 | 0.210 | 2.820 | 1.832 |

Normalized | 0.967060115 | 1 | 0.880851064 | 0.991812227 |

LOE: | ||||

Direct Solution | 3.465 | 0.210 | 2.244 | 1.780 |

Normalized | 1.016738817 | 1 | 1.106951872 | 1.020786517 |

Modal Solution | 3.454 | 0.214 | 2.203 | 1.779 |

Normalized | 1.019976838 | 0.981308411 | 1.127553336 | 1.021360315 |

## Reference

NAFEMS R0016 - Selected Benchmarks for Forced Vibration, J Maguire, D J, Dawswell, L Gould 1989