OS-V: 0385 Simply-Supported Thick Square Plate Transient Forced Vibration Response

Test 21T OptiStruct is used to investigate the Peak Displacement in z-direction, the time at the peak displacement, extreme fiber bending stress at undamped Natural Frequency and the Static displacement 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 suddenly applied step load F0=106 N/m2 is induced in the z-direction. For modal analysis solution, a damping ratio of 0.02 is applied in all 16 modes at a time step of 0.0001 secs and for direct solution, Rayleigh damping factor α1=5.772 and α2=6.929×10-5 at a time step of 0.0001 secs 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) Time at Peak Displacement (sec) Peak Stress (N/mm2) Static Displacement (mm)
Reference Solution 4.524 0.0108 62.11 2.333
Direct Solution 4.838 0.011 72.67 2.42
Normalized 0.935097148 0.981818182 0.854685565 0.964049587
Modal Solution 4.870 0.011 75.16 2.42
Normalized 0.928952772 0.981818182 0.82637041 0.964049587
Direct Solution 4.604 0.0108 57.98 2.34
Normalized 0.982623805 1 1.071231459 0.997008547
Modal Solution 4.611 0.0107 58.44 2.341
Normalized 0.981132075 1.009345794 1.062799452 0.996582657

Model Files

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

The model files used in this problem include:
  • Test21THOED.fem
  • Test21THOEM.fem
  • Test21TLOED.fem
  • Test21TLOEM.fem


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