# OS-V: 0365 Simply-Supported Thin Square Plate Transient Forced Vibration Response

Test 13T 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.

## Model Files

Before you begin, copy the file(s) used in this problem to your working directory.

## Benchmark Model

The 2nd order and 1st order quad elements are used to model the square plate of thickness 0.05 m. 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 = 100 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 0.002 secs and for direct solution, Rayleigh damping factor α1 = 0.299 and α2 = 1.339×10-3 at a time step of 0.002 secs 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) Time at Peak Displacement (sec) Peak Stress (N/mm2) Static Displacement (mm)
Reference Solution 3.523 0.210 2.484 1.817
HOE:
Direct Solution 3.637 0.212 2.784 1.832
Normalized 0.968655485 0.990566038 0.892241379 0.991812227
Modal Solution 3.643 0.210 2.820 1.832
Normalized 0.967060115 1 0.880851064 0.991812227
LOE:
Direct Solution 3.465 0.210 2.244 1.780
Normalized 1.016738817 1 1.106951872 1.020786517
Modal Solution 3.454 0.214 2.203 1.779
Normalized 1.019976838 0.981308411 1.127553336 1.021360315

## Reference

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