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Comparison with Euler-Bernoulli Theory

From our PreAnalysisPre-Analysis, based on Euler-Bernoulli beam theory, we calculated frequencies of 17.8, 111.5 and 312.1 Hz . Our ANSYS simulation yielded results of for the first three bending modes. The ANSYS frequencies for the first three bending modes are 17.7, 107.0 and 179285.2 Hz. Note that in the ANSYS results, the third mode is NOT a bending mode. So the fourth mode reported by ANSYS is the third bending mode. These results give percent differences of 0.6%, 4.2% and 74%. Our and 8.7% between ANSYS and theory. So the ANSYS results match well for the first two modes, but are way off for the third mode. This is explained by the inaccuracy of quite well with Euler-Bernoulli beam theory. Note that the ANSYS beam element formulation used here is based on Timoshenko beam theory which includes shear-deformation effects (this is neglected in the Euler-Bernoulli beam theory for high order modes in short, stubby beams).

Comparison with refined mesh

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