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.



Figure 1. FE Model with Boundary Conditions and Loadcases

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
ρ
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

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

The model file used in this problem includes:

fv4.fem

Reference

NAFEMS R0015 - Selected benchmarks for natural frequency analysis