Modal Analysis of a Beam with Axial Load

This test lets you check analysis results for a beam with a static preload. You will use a 1D mesh.

Reference:

SFM, Afnor Technique, Guide de validation des prologiciels de calcul de structures, pp192-193.
 

Specifications

Geometry Specifications

Length:
L = 2 m

Width and height:
a = 0.05 m

Area:
2.5e-3 m2

Inertia:
Iz = 5.2083e-007 m4


Analysis Specifications

Young Modulus (material):
E = 2e+011 N_m2

Poisson's Ratio (material):
ν = 0.3

Density:
ρ = 7800 kg/m3

Mesh Specifications:
10 elements

Restraints (User-defined):
A: Tx = Ty = 0
B: Ty = 0

Loads:
The distributed force Fx is a static pressing preload in the axis of the beam.
There is two cases of preloading:

  • |Fx| = 0

  • |Fx| = 105 N
 

Results

  • The analytical solution is:


 

  • The table below presents the analysis results. Relative errors are listed:

Load

Fundamental natural mode of vibration

Frequencies [Hz]

Relative errors [%]

 Analytical results

 Computed results

|Fx|=0

Bending mode 1

28.702

28.694

0.03

Bending mode 2

114.807

114.701

0.09

|Fx|=105N

Bending mode 1

22.434

22.428

0.03

Bending mode 2

109.08

108.981

0.09

To Perform the Test:

The Modal_analysis_beam_with_axial_load.CATAnalysis document presents a complete analysis of this case, computed with a load of 105 N.

To compute this case, proceed as follow:

  1. Open the CATAnalysis document.

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

To compute the unloaded case, change in this CATAnalysis the value of the distributed force.