SS-V: 6040 Simply Supported Thin Square Plate - Random Forced Vibration Response

Test No. VD05View random response of a simply supported square plate subjected to uniform forced vibration.


A simply supported thin square plate 10 x 10 x 0.05 m is subject to uniform pressure P=100 Pa which forces random vibrations with uniform Power Spectral Density function ("white noise").

Figure 1.

Sixteen (16) modes are used to approximate dynamics solution and 2% modal damping is assumed in all modes.

The material properties are:
Modulus of Elasticity
2.e+11 Pa
Poisson's Ratio
8.e+3 kg/m3


The plate is simulated as a 3D solid body. Spot-lines were created at the mid-plane of the plate in order to apply hinge supports (Figure 2).
Figure 2.

Peak response is reached when excitation frequency becomes equal to first natural frequency of the plate. Figure 3 shows PSD response for Y-displacement in picked point with coordinates [m] X = 4.9627, Y = 0.05, Z = -5.0418.

Figure 3.

Figure 4. Distribution of Y-displacement PSD
The following table contains peak response comparison.
PSD Y-displacement,


PSD Surface Stress X,


2081 1028.2 SimSolid, 3D Solid model
2063.2 1025.44 Reference, thin plate model
1 Test 13H from NAFEMS Publication R0016, “Selected Benchmarks for Forced Vibration” J. Maguire, D.J. Dawswell, L. Gould