OS-V: 0400 Pin-ended Double Cross
Test No. FV2 A pin-ended double cross, in-plane vibration problem. OptiStruct is used to investigate the coupling between flexural and extensional behavior, as well as the repeated and closed eigenvalues of the double cross in Normal Modes Analysis.
Figure 1.
Benchmark Model
The 2-node simple beam elements are used to model the double cross. Each arm of the cross consists of four elements. The x- and y-translation displacements are fixed at the end of all arms.
The material properties are:
- E
- 200 x 109 N/m2
- 8000 kg/m3
Modal Analysis Results
The frequency of each targeted mode is normalized with the closed form solution.
f*- Closed form solution
| Mode 1 | Modes 2 and 3 | Modes 4, 5, 6, 7 and 8 | |||
|---|---|---|---|---|---|
 |
 |
 |
|||
f* CBAR |
11.336 Hz 0.9984 |
f* CBAR |
17.709 Hz 0.9958 |
f*CBAR |
17.709 Hz 0.9974 |
| Mode 9 | Modes 10 and 11 | Modes 12, 13, 14, 15 and 16 | |||
|---|---|---|---|---|---|
 |
 |
 |
|||
f*
CBAR |
45.345 Hz 1.0000 |
f* CBAR |
57.390 Hz .9944 |
f*CBAR |
57.390 Hz 0.9999 |
Model Files
The model files used in this problem include:
- <install_directory>/hwsolvers/demos/optistruct/verification/fv2.fem
Reference
NAFEMS Ltd, The Standard NAFEMS BENCHMARKS TNSB Rev. 3, NAFEMS Ltd, Scottish Enterprise Technology Park, Whitworth Building, East Kilbride, Glasgow, United Kingdom, 1990.