# 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.

## 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:
Property
Value
E
200 x 109 N/m2
$\rho$
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 file used in this problem includes:

fv2.fem

## Reference

NAFEMS R0015 - Selected benchmarks for natural frequency analysis