OS-V: 0375 Simply-Supported Thick Square Plate Periodic Forced Vibration Response
Test 21P OptiStruct is used to investigate the Peak Displacement in z-direction and extreme fiber bending stress 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 0.05m. 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 harmonic forced vibration F=F_{0} (sin ωt-sin 3ωt) is induced in the z-direction. (F_{0}=10^{6} N/m^{2} over whole plate, ω=2πf, f=20 Hz). For modal analysis solution, a damping ratio of 0.02 is applied in all 16 modes and for direct solution, Rayleigh damping factor α_{1}=5.772 and α_{2}=6.929×10^{-5} 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) | Peak Stress (N/mm^{2}) | |
---|---|---|
Reference Solution | 4.929 | 67.67 |
HOE: | ||
Direct Solution | 5.134 | 79.26 |
Normalized | 0.960070121 | 0.853772395 |
Modal Solution | 5.134 | 79.291 |
Normalized | 0.960070121 | 0.8534386 |
LOE: | ||
Direct Solution | 5.016 | 65.48 |
Normalized | 0.982655502 | 1.033445327 |
Modal Solution | 5.018 | 65.595 |
Normalized | 0.98226385 | 1.031633509 |
Model Files
The model files used in this problem include:
- /Test21PHOED.fem
- /Test21PHOEM.fem
- /Test21PLOED.fem
- /Test21PLOEM.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.