# SS-V: 6000 Simply Supported Thin Square Plate - Harmonic Forced Vibration Response

Test No. VD01View transient response of a simply supported square plate subjected to harmonic 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 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.

The excitation frequency changes in range from 0 to just above first resonant frequency of the plate.

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 1).
Peak response is reached when excitation frequency becomes equal to first natural frequency of the plate. It occurs 19.82 seconds after the beginning of the excitation.
The following table contains peak response comparison.
Deflection Y, mm Surface Stress, MPa
45.34 31.86 SimSolid, 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