OS-V: 0350 Simply-Supported Thin Square Plate Periodic Forced Vibration Response

Test 13P 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

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-sin 3ωt) is induced in the z-direction. (F0 = 100 N/m2 over whole plate, ω = 2πf, f = 1.2 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
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 2.863 2.018
Direct Solution 2.928 2.418
Normalized 0.977800546 0.834574028
Modal Solution 2.929 2.426
Normalized 0.977466712 0.831821929
Direct Solution 2.825 1.956
Normalized 1.013451327 1.031697342
Modal Solution 2.826 1.961
Normalized 1.013092711 1.029066803


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