# OS-V: 0330 Deep Simply-Supported Beam Transient Forced Vibration Response

Test 5T OptiStruct is used to investigate the Peak Displacement in y-direction, the time at the peak displacement, extreme fiber bending stress at undamped Natural Frequency and the Static displacement at the mid-span node.

## Benchmark Model

Timoshenko beam and Engineer’s beam elements are used to model the simply-supported beam
which consists of 10 elements. The displacements in x, y, and z direction, as well as the
rotation in x direction are fixed at the end A. In addition, the displacements in y and z
direction are constrained at end B. A suddenly applied step load
F_{0}=10^{6} N/m is induced in the y-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}=5.36 and
α_{2}=7.46×10^{-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 | 1.043 | 0.0117 | 18.76 | 0.538 |

HOE: | ||||

Direct Solution | 1.036 | 0.0116 | 18.02 | 0.533 |

Normalized | 1.006756757 | 1.00862069 | 1.041065483 | 1.009380863 |

Modal Solution | 1.03 | 0.0115 | 17.99 | 0.533 |

Normalized | 1.012621359 | 1.017391304 | 1.042801556 | 1.009380863 |

LOE: | ||||

Direct Solution | 0.94 | 0.0109 | 18.02 | 0.48 |

Normalized | 1.109574468 | 1.073394495 | 1.041065483 | 1.120833333 |

Modal Solution | 0.939 | 0.01109 | 17.92 | 0.48 |

Normalized | 1.110756124 | 1.055004509 | 1.046875 | 1.120833333 |

## Model Files

The model files used in this problem include:

- /Test5TPBEAMLD.fem
- /Test5TPBEAMLM.fem
- /Test5TPBEAMD.fem
- /Test5TPBEAMM.fem

## Reference

NAFEMS Ltd, The Standard NAFEMS BENCHMARKS TNSB Rev. 3, NAFEMS Ltd, Scottish Enterprise Technology Park, Whitworth Building, East Kilbride, Glasgow, United Kingdom, 1990.