OS-V: 0395 Simply-Supported Thick Square Plate Random Forced Vibration Response
Test 21R OptiStruct is used to investigate the Peak Displacement in z-direction and extreme fiber bending stress at undamped Natural Frequency (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 steady state random forcing with uniform power spectral density (of force) PSD= (106 N/m2)2/Hz is induced in the z-direction. For modal analysis solution, a damping ratio of 0.02 is applied in all 16 modes and for direct solution, Rayleigh damping factor α1=5.772 and α2=6.929×10-5 are given.
- Young’s Modulus
- 200 × 109 N/m2
- Poisson’s Ratio
- 0.3
- Density
- 8000 kg/m3
Frequency Response Summary
f*
- Closed form solution
Peak Displacement PSD (mm2/Hz) | Peak Stress PSD ((N/mm2)2 | Frequency (Hz) | |
---|---|---|---|
Reference Solution | 3401.81 | 641200.00 | 45.90 |
HOE: | |||
Direct Solution | 3929.62 | 892303.43 | 45.24 |
Normalized | 0.865684214 | 0.718589639 | 1.014588859 |
Modal Solution | 3928.88 | 892421.36 | 45.27 |
Normalized | 0.865847264 | 0.718494681 | 1.013916501 |
LOE: | |||
Direct Solution | 3607.25 | 600979.1 | 45.62 |
Normalized | 0.943048028 | 1.066925622 | 1.006137659 |
Modal Solution | 3606.23 | 600094.2 | 45.63 |
Normalized | 0.943314764 | 1.068498912 | 1.00591716 |
Model Files
The model files used in this problem include:
- /Test21RHOED.fem
- /Test21RHOEM.fem
- /Test21RLOED.fem
- /Test21RLOEM.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.