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.

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 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
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 (mm) Peak Stress (N/mm2)
Reference Solution 4.929 67.67
Direct Solution 5.134 79.26
Normalized 0.960070121 0.853772395
Modal Solution 5.134 79.291
Normalized 0.960070121 0.8534386
Direct Solution 5.016 65.48
Normalized 0.982655502 1.033445327
Modal Solution 5.018 65.595
Normalized 0.98226385 1.031633509

Model Files

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

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


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