OS-V: 0420 Free Thin Square Plate

Test No. FV12 A thin square plate model, which contains three rigid body modes. OptiStruct investigates the repeated eigenvalues and kinematically incomplete suppressions of the thin plate in Normal Modes Analysis.


fv12
Figure 1. FE Model with Boundary Conditions and Loadcases

Benchmark Model

The 4-node quad elements with 8x8 mesh configuration are used to model the plate. The x-translation, y-translation displacements and z-rotational displacements are fixed for all nodes.

The material properties are:
Property
Value
E
200 x 109 N/m2
υ
0.3
ρ
8000 kg/m3

Modal Analysis Results

The frequency of each targeted mode is normalized with the closed form solution. The closed form solution is not available for mode 10, use target value for H.O.E. instead.
f*
Closed form solution
S# Mode # OptiStruct Results F* (Hz) Normalized Value
1 Mode 4 1.619 1.622 0.9981
2 Mode 5 2.394 2.360 1.0144
3 Mode 6 2.9896 2.922 1.0231
4 Mode 7 and 8 4.2315 4.233 0.9996
5 Mode 9 7.8002 7.416 1.0518
6 Mode 10 (HOE) 7.8848 7.392 1.0667
Mode 4 Mode 5 Mode 6
fv12a fv12b fv12c
f*

CQUAD4

 1.622 Hz

0.9964

 f*

CQUAD4

 2.360 Hz

1.0145

 f*

CQUAD4

 2.922 Hz

1.0231
Modes 7 and 8 Mode 9 Mode 10
../../images/solvers/fv12d.png fv12e fv12f
f*

CQUAD4

 4.233 Hz

0.9978

 f*

CQUAD4

 7.416 Hz

1.0496

 F[HOE]

CQUAD4

 7.392 Hz

1.1746

Model Files

Refer to Access the Model Files to download the required model file(s).

The model file used in this problem includes:

fv12.fem

Reference

NAFEMS R0015 - Selected benchmarks for natural frequency analysis