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Natural Frequencies of Elastic Cantilevered Beams

Natural Frequencies of Elastic Cantilevered Beams. By Chris Klobedanz MANE-4240 Final Project. 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

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Natural Frequencies of Elastic Cantilevered Beams

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  1. Natural Frequencies of Elastic Cantilevered Beams 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 • Use Euler-Bernoulli Beam Theory: • Incorporate Boundary Conditions: • Determine the Natural Frequencies fn: • where • kn is determined as the root of:

  4. 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

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

  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

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