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.

P = 100 ∗ sin ( ω ∗ t ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8qrps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaake aacaWGqbGaeyypa0JaaGymaiaaicdacaaIWaGaey4fIOIaci4Caiaa cMgacaGGUbWaaeWaaeaacqaHjpWDcqGHxiIkcaWG0baacaGLOaGaay zkaaaaaa@45C6@

Where,
ω = 2 ∗ P I ∗ f MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8qrps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaake aacqaHjpWDcqGH9aqpcaaIYaGaey4fIOIaamiuaiaadMeacqGHxiIk caWGMbaaaa@40B2@
f MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8qrps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaake aacaWGMbaaaa@39A2@
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).
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.
Figure 2.


Figure 3.


The following table contains peak response comparison.
Table 1.
Deflection Y Amplitude, mm Surface Stress Amplitude, MPa
45.68 32.08 SimSolid, 3D solid model
45.42 35.08 Reference1, thin plate model
1 Test 13H from NAFEMS Publication R0016, “Selected Benchmarks for Forced Vibration” J. Maguire, D.J. Dawswell, L. Gould