# OS-V: 0425 Clamped Thin Rhombic Plate

Test No. FV15 The behavior of distorted thin elements in normal modes analysis is examined using OptiStruct.

## Benchmark Model

The 4-node quad elements with 12x12 mesh configuration are used to model the thin rhombic plate. The x-translation, y-translation displacements, and z-rotational displacements are fixed for all of the nodes. In addition, the z-translation, x-rotational and y-rotational are fixed for the nodes along the four edges.

The material properties are:
Property
Value
E
200 x 109 N/m2
$\upsilon$
0.3
$\rho$
8000 kg/m3

## Modal Analysis Results

The frequency of each targeted mode is normalized with the closed form solution. If a closed form solution is not available, the target values for H.O.E. are used instead. All benchmarked results are normalized with target values.
f*
Closed form solution
Mode 1 Mode 2 Mode 3
f*

7.938 Hz

0.9798

f*

12.835 Hz

1.0079

f*

17.941 Hz

1.0182

Mode 4 Mode 5 Mode 6
f*

19.133 Hz

0.9629

f*

24.009 Hz

1.0339

f*

27.922 Hz

1.0036

## Model Files

The model file used in this problem includes:

fv15.fem

## Reference

NAFEMS R0015 - Selected benchmarks for natural frequency analysis