# SS-V: 6010 Simply Supported Thin Square Plate - Periodic Forced Vibration Response

Test No. VD02View transient response of a simply supported square plate subjected to periodic 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)
$P=100*\left(\mathrm{sin}\left(\omega \ast t\right)-\mathrm{sin}\left(3\omega \ast t\right)\right)$
Where,
$\omega =2\ast PI\ast f$
$f=1.2Hz$
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

## 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). In order to simulate periodic load changing according to the formula above, two pressure loads were applied to the plate:
• $P=100\ast \mathrm{sin}\left(\omega \ast t\right)$ to the top surface of the plate, and
• $P=-100\ast \mathrm{sin}\left(3\omega \ast t\right)$ to the bottom surface of the plate
The following table contains typical values at steady-state portion of the dynamics solution (Figure 2).
Deflection Y, mm Surface Stress, MPa
-2.886 2.062 SimSolid, solid model
-2.863 2.018 Reference, thin plate model
1 Test 13P from NAFEMS Publication R0016, “Selected Benchmarks for Forced Vibration” J. Maguire, D.J. Dawswell, L. Gould