OS-V: 0340 Simply-Supported Thin Square Plate Harmonic Forced Vibration Response

Test 13H 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


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 steady-state harmonic forced vibration F = F0 sin ωt is induced in the z-direction. (F0 = 100 N/m2 over whole plate, ω = 2ωf, f = 0 to 4.16 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 = 0.299 and α2 = 1.339×10-3 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) Frequency (HZ)
Reference Solution 45.42 30.03 2.377
HOE:
Direct Solution 47.254 37.57 2.323
Normalized 0.961188471 0.799307958 1.023245803
Modal Solution 47.34 37.64 2.324
Normalized 0.959442332 0.797821467 1.022805508
LOE:
Direct Solution 45.22 30.84 2.349
Normalized 1.004422822 0.973735409 1.011919966
Modal Solution 45.45 30.98 2.345
Normalized 0.999339934 0.969335055 1.013646055

Reference

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