Post on 23-Dec-2015
By Chris Klobedanz
MANE-4240 Final Project
Natural Frequencies of Elastic
Cantilevered Beams
Purpose• Evaluate the Natural Frequencies of a Steel
Cantilever Beam System• Compare the Results of Beams with Different
Cross-Sectional Areas: Square, Circle, I-Beam
• Compare the Exact Solution to Finite Element Models in Ansys and Comsol
• Compare Different Mesh Configurations within the Finite Element Models
Analytic Solution• Use Euler-Bernoulli Beam Theory:
• Incorporate Boundary Conditions:
• Determine the Natural Frequencies fn: where
• kn is determined as the root of:
Comsol Models• Build a 3D Eigenfrequency Model and Compare
Extra Coarse, Normal, and Extra Fine Meshes:
Extra Coarse Block Normal Cylinder
Extra Fine I-Beam
Ansys Models• Build a 1D Linear Elastic Model with 3-Noded
Beam Elements• Run a Modal Analysis• Compare 5, 10, and 20 Element Meshes
20 Element Model
Results
Comsol
Ansys
Analytic
* The Deformed Beam Models look similar for block, cylinder, and I-beam models
Results (cont.)
Conclusions• Comsol and Ansys are very accurate at estimating
the lower order natural frequencies, but get increasingly more inaccurate at each subsequent frequency
• Comsol and Ansys are more accurate at estimating the natural frequencies of less complicated models. The block and cylinder models had much less error than the I-beam models
• Ansys had more accurate results than Comsol at the expense of taking more time to build the models
• With more input, it is possible that both programs could converge to more accurate solutions