Test No. VD05 View random response of a simply
supported square plate subjected to uniform forced vibration.
Definition
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:
Properties
Value
Modulus of Elasticity
2.e+11 Pa
Poisson's Ratio
0.3
Density
8.e+3 kg/m3
Results
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,
mm2/Hz
PSD Surface Stress X,
MPa2/Hz
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
