1. By Chris Klobedanz MANE-4240 Final Project

2. 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

3. Analytic Solution

4. Comsol Models Build a 3D Eigenfrequency Model and Compare Extra Coarse, Normal, and Extra Fine Meshes: Extra Coarse BlockNormal Cylinder Extra Fine I-Beam

5. 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

6. Results Comsol Ansys Analytic * The Deformed Beam Models look similar for block, cylinder, and I-beam models

7. Results (cont.)

8. 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