# OS-V: 0385 Simply-Supported Thick Square Plate Transient Forced Vibration Response

Test 21T 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.

## Benchmark Model

The 2nd order and 1st order quad elements are used to model the square plate of thickness
1.0m. 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}=10^{6} 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
0.0001 secs and for direct solution, Rayleigh damping factor α_{1}=5.772 and
α_{2}=6.929×10^{-5} at a time step of 0.0001 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 | 4.524 | 0.0108 | 62.11 | 2.333 |

HOE: | ||||

Direct Solution | 4.838 | 0.011 | 72.67 | 2.42 |

Normalized | 0.935097148 | 0.981818182 | 0.854685565 | 0.964049587 |

Modal Solution | 4.870 | 0.011 | 75.16 | 2.42 |

Normalized | 0.928952772 | 0.981818182 | 0.82637041 | 0.964049587 |

LOE: | ||||

Direct Solution | 4.604 | 0.0108 | 57.98 | 2.34 |

Normalized | 0.982623805 | 1 | 1.071231459 | 0.997008547 |

Modal Solution | 4.611 | 0.0107 | 58.44 | 2.341 |

Normalized | 0.981132075 | 1.009345794 | 1.062799452 | 0.996582657 |

## Model Files

Refer to Access the Model Files to download the required model file(s).

- Test21THOED.fem
- Test21THOEM.fem
- Test21TLOED.fem
- Test21TLOEM.fem

## Reference

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