F-02 (2D Truss Vibration) |
  
|
F-02 (2D Truss Vibration) |
|
Objective
To verify the behavior of truss element vibration
Problem Description
The 2D truss structure [Ref 1] shown below vibrates under its own weight. Nodal coordinates in meters are shown in parenthesis.
Material properties: E = 7.17e10 N/m2, ν = 0.30, ρ = 2768 Kg/m3
Section cross-sectional areas
Vertical trusses: 8.0e-5 m2
Horizontal trusses: 6.0e-5 m2
Diagonal trusses: 4.0e-5 m2
Finite Element Model
15 beam elements
Model type: 2D Truss
Results
The mode frequencies are given by [Ref 1]
Unit: mode frequency – Hz
Mode Frequency |
ENERCALC 3D |
[Ref 1] |
Mode 1 |
7.9822 |
7.9832 |
Mode 2 |
27.9952 |
28.0012 |
Mode 3 |
44.8770 |
44.8815 |
Mode 4 |
49.5731 |
49.5859 |
Mode 5 |
94.9018 |
94.925 |
Mode 6 |
116.3799 |
116.3882 |
Mode 7 |
125.6432 |
125.6551 |
Mode 8 |
126.1574 |
126.1727 |
Mode 9 |
132.1162 |
132.1308 |
Mode 10 |
152.2912 |
152.3021 |
Comments
The vibration frequencies given by ENERCALC 3D are very close to the referenced values.
Reference
[1]. Stejskal, Dehombreux, Eiber, Gupta, Okrouhlik, “Mechanics with Matlab” April 2001
Web: http://www.geniemeca.fpms.ac.be/mechmatHTML/
