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).

Figure 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 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.

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

Frequency Response Summary

The frequency of each targeted mode is normalized with the closed form solution.
Closed form solution
  Peak Displacement PSD (mm2/Hz) Peak Stress PSD ((N/mm2)2 Frequency (Hz)
Reference Solution 3401.81 641200.00 45.90
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
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

Refer to Access the Model Files to download the required model file(s).

The model files used in this problem include:
  • Test21RHOED.fem
  • Test21RHOEM.fem
  • Test21RLOED.fem
  • Test21RLOEM.fem


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