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.



図 1. FE Model with Boundary Conditions and Loadcases

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-sin 3ωt) is induced in the z-direction. (F0=106 N/m2 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 α1=5.772 and α2=6.929×10-5 are given.

The material properties are:
Material Properties
Value
Young’s Modulus
200 × 109 N/m2
Poisson’s Ratio
0.3
Density
8000 kg/m3

Frequency Response Summary

The frequency of each targeted mode is normalized with the closed form solution.
f*
Closed form solution
  Peak Displacement (mm) Peak Stress (N/mm2)
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

必要なモデルファイルのダウンロードについては、モデルファイルへのアクセスを参照してください。

The model files used in this problem include:
  • Test21PHOED.fem
  • Test21PHOEM.fem
  • Test21PLOED.fem
  • Test21PLOEM.fem

Reference

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