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Author: John Singleton, Cornell University
Problem Specification
1. Pre-Analysis & Start-Up
2. Geometry
3. Mesh
4. Setup (Physics)
5. Solution
6. Results
7. Verification and Validation
Exercises
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7. Verification and Validation
For our verification, we will focus on the first 3 modes. ANSYS uses a different type of beam element to compute the modes and frequencies, which provides more accurate results for relatively short, stubby beams such as the one examined in this tutorial. However, for these beams, the Euler-Bernoulli beam theory breaks down and is no longer valid for higher order modes.
Verification
Comparison with Euler-Bernoulli Theory
From our PreAnalysis, based on Euler-Bernoulli beam theory, we calculated frequencies of 17.8, 111.5 and 312.1 Hz. Our ANSYS simulation yielded results of 17.7, 107.0 and 179.2 Hz. These results give percent differences of 0.6%, 4.2% and 74%. Our results match well for the first two modes, but are way off for the third mode. This is explained by the inaccuracy of Euler-Bernoulli beam theory for high order modes in short, stubby beams.
Comparison with refined mesh
Next, let's check our results with a more refined mesh. We'll run the simulation with 25 elements instead of 10. Following the steps outlined in the Mesh Refinement section of the Cantilever Beam Verification and Validation, refine the mesh.
Meshing the beam with 25 elements yielded the following modal frequencies:
These modal frequencies are all very close to those computed with a mesh of 10 elements, meaning that our solution is mesh converged.
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