ES01: Vibrations of Axially Loaded Beam - Nonlinear
- Gokhan Alkan (Unlicensed)
A beam is subjected to the action of self-weight and an axial compressive force P. The beam is 80 inches long and pinned at both ends. The magnitude of the axial compressive load is 40,000 lbs. The weight of the beam is considered and the weight density is 0.281 lb/in3. The beam has a square cross-section of 2 x 2 inches.
Determine the axial deflection and maximum stress under static loading. Use the results to determine the first three natural frequencies of the structure and the slope at the left-hand support. Eigenvalue analysis uses the stiffness matrix of the deformed and stressed structure.
The model is selected with enough elements to characterize the dynamic behavior.
The axial load is applied at joint 14 in the negative X direction.
If the stress stiffening (geometric nonlinearity) is ignored, the natural frequency of the structure would be 28.76 hz instead of the 17.07 hz.
Tested Features
Sources
- LARSA 4D
- Timoshenko, S., and Young,D.H., "Vibration Problems in Engineering", 3rd Edition, D. Van Nostrand Co.,Inc., New York, 1955, p. 374.