OS-V: 0340 Simply-Supported Thin Square Plate Harmonic Forced Vibration Response
Test 13H 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).
![](../../../images/solvers/nafems_simply_supported_thin_square_plate_harmonic_force.png)
図 1.
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=F0 sin ωt is induced in the z-direction. (F0=100 N/m2 over whole plate, ω=2ωf, f=0 to 4.16 Hz). For modal analysis solution, a damping ratio of 0.02 is applied in all 16 modes and for direct solution, Rayleigh damping factor α1=0.299 and α2=1.339×10-3 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 (mm) | Peak Stress (N/mm2) | Frequency (HZ) | |
---|---|---|---|
Reference Solution | 45.42 | 30.03 | 2.377 |
HOE: | |||
Direct Solution | 47.254 | 37.57 | 2.323 |
Normalized | 0.961188471 | 0.799307958 | 1.023245803 |
Modal Solution | 47.34 | 37.64 | 2.324 |
Normalized | 0.959442332 | 0.797821467 | 1.022805508 |
LOE: | |||
Direct Solution | 45.22 | 30.84 | 2.349 |
Normalized | 1.004422822 | 0.973735409 | 1.011919966 |
Modal Solution | 45.45 | 30.98 | 2.345 |
Normalized | 0.999339934 | 0.969335055 | 1.013646055 |
Model Files
The model files used in this problem include:
- /Test13HHOED.fem
- /Test13HHOEM.fem
- /Test13HLOED.fem
- /Test13HLOEM.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.