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

Test No. VD04 View 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.

$$P=100\ast \mathrm{sin}\left(\omega \ast t\right)$$

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/m
^{3}

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 | 32.08 | 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