# SS-V: 6030 Simply Supported Thin Square Plate - Frequency Response

Test No. VD04View frequency response of a simply supported square plate.

## Definition

A simply supported thin square plate 10 x 10 x 0.05 m is subject to uniform pressure P=100 Pa which changes in time as the following function.(1)
$P=100\ast \mathrm{sin}\left(\omega \ast t\right)$
Where,
$\omega =2\ast PI\ast f$
$f$
Excitation frequency.

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
Note: This test is similar to Test VD01, but it is solved in frequency domain.

## 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 1).
Peak response is reached when excitation frequency becomes equal to first natural frequency of the plate. Figure 2 shows frequency sweep result for Y-displacement amplitude in picked point with coordinates [m] X = 4.9469, Y = 0.05., Z = -4.9158.
The following table contains peak response comparison.
Deflection Y Amplitude, mm Surface Stress Amplitude, MPa
45.68 32.52 SimSolid, 3D solid model
45.42 35.08 Reference, thin plate model
1 Test 13H from NAFEMS Publication R0016, “Selected Benchmarks for Forced Vibration” J. Maguire, D.J. Dawswell, L. Gould