Cantilever Beam with Eccentric Point Masses

The purpose of this test is to check the coupling between torsional and flexural behavior. You will use a 1D beam.

Reference:

NAFEMS-Glasgow, Benchmark newsletter, p.15, April 1989.

 

Specifications

Geometry Specifications

Length:
L = 10 m   

Section (circular):
D = 0.5 m

Mass 1 (center):

  • x = 10 m
    y = 2 m
  • M1 = 10000 kg

Mass 2 (center):  

  • x = 10 m
    y = 2 m
  • M2 = 1000 kg


Analysis Specifications

Young Modulus (material):
E = 200 GPa


View of the mode 7

Poisson's Ratio (material):
ν = 0.3

Mesh Specifications:

  • 5 beam elements along the cantilever

  • To define the rigid bar between the two masses,  
    use a General Analysis Connection and a
    User-defined Connection Property (Rigid as Middle option).

Restraints (User-defined):
At end 1, Tx = Ty = Tz = Rx = Ry = Rz = 0

 

Results

The results are based on the 6 lowest normal modes of the structure.
The results and the percentage of errors are listed in the table below:

Mode

Exact [Hz]

Beam [Hz]

Error [%]

1

1.723

1.722

0.058

2

1.727

1.725

0.116

3

7.413

7.410

0.040

4

9.972

9.946

0.261

5

18.160

18.046

0.628

6

26.972

26.697

1.020

To Perform the Test:

The cantilever_beam_excentric_point_masses.CATAnalysis document presents a complete analysis of this case, computed with a mesh formed of beam elements. Proceed as follow:

  1. Open the CATAnalysis document.

  2. Compute the case and generate an image called Deformed mesh.