# OS-V: 0410 Cantilever with Off-Center Point Masses

Test No. FV4 The problem is set up to test the behavior of coupling between torsional and flexural, off-center inertial axis, and close eigenvalues. OptiStruct is used in this normal modes analysis.

## Benchmark Model

The 2-node simple beam elements are used to model the problem. The cantilever beam consists of five elements. Two rigid elements are used to connect mass 1, 10000 kg, and mass 2, 1000 kg, at the end of the cantilever beam. All degrees of freedom at end A are constrained.

The material properties for the cantilever beam 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 Mode 2 Mode 3
f*

CBAR

1.723 Hz

1.0054

f*

CBAR

1.727 Hz

1.0048

f*

CBAR

7.413 Hz

1.008

Mode 4 Mode 5 Mode 6
f*

CBAR

9.972 Hz

1.0055

f*

CBAR

18.155 Hz

1.0067

f*

CBAR

26.957 Hz

1.0068

## Model Files

The model file used in this problem includes:

fv4.fem

## Reference

NAFEMS R0015 - Selected benchmarks for natural frequency analysis