Analysis of thin-walled beams with variable monosymmetric cross section by means of Legendre polynomials
et | 26 mars 2019
À propos de cet article
Article Category: Research Article
Publié en ligne: 26 mars 2019
Pages: 1 - 12
Reçu: 20 nov. 2018
Accepté: 02 janv. 2019
DOI: https://doi.org/10.2478/sgem-2019-0001
Mots clés
© 2019 Józef Szybiński, Piotr Ruta, published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.
Figure 1
Figure 2
Figure 3
Figure 4
Eigenfrequencies in case of clamped-clamped support (C-C) [Hz].
| Mode number | Paper dim = 10 | Paper dim = 15 | Paper dim = 20 | FEM SOFiSTiK beam element 7DOF d = 20 | FEM SOFiSTiK beam element 7DOF d = 25 | FEM SOFiSTiK beam element 7DOF d = 50 | FEM Abaqus shell elements (quad) |
|---|---|---|---|---|---|---|---|
| 1 | 10.17 | 10.15 | 10.15 | 10.17 | 10.16 | 10.15 | 10.05 |
| 2 | 18.43 | 18.39 | 18.39 | 17.93 | 17.92 | 17.89 | 18.18 |
| 3 | 26.70 | 26.68 | 26.68 | 26.83 | 26.75 | 26.64 | 26.11 |
| 4 | 48.69 | 48.70 | 48.69 | 47.62 | 47.45 | 47.20 | 46.79 (lf) |
| 5 | 52.71 | 50.72 | 50.72 | 49.49 | 49.41 | 49.31 | 48.18 |
| 6 | 53.11 | 52.92 | 52.92 | 51.86 | 51.57 | 51.17 | 49.32 |
| 7 | 90.71 | 82.42 | 82.34 | 83.58 | 82.66 | 81.43 | 67.38 (lf) |
| 8 | 96.80 | 93.59 | 93.59 | 94.05 | 93.45 | 92.64 | 85.73 (lf) |
Eigenfrequencies in case of clamped-free support (C-F) [Hz].
| Mode number | Paper dim = 10 | Paper dim = 15 | Paper dim = 20 | FEM SOFiSTiK beam element 7DOF d = 20 | FEM SOFiSTiK beam element 7DOF d = 25 | FEM SOFiSTiK beam element 7DOF d = 50 | FEM Abaqus shell elements (quad) |
|---|---|---|---|---|---|---|---|
| 1 | 2.20 | 2.19 | 2.20 | 2.15 | 2.15 | 2.15 | 2.19 |
| 2 | 8.33 | 7.68 | 7.60 | 7.68 | 7.69 | 7.69 | 7.55 |
| 3 | 13.44 | 12.96 | 12.91 | 12.26 | 12.25 | 12.24 | 12.77 |
| 4 | 14.42 | 13.88 | 13.85 | 13.66 | 13.67 | 13.68 | 13.77 |
| 5 | 24.31 | 23.18 | 23.13 | 23.97 | 23.95 | 23.93 | 22.75 |
| 6 | 35.95 | 32.68 | 32.54 | 31.07 | 31.00 | 30.90 | 30.89 |
| 7 | 44.18 | 50.31 | 50.21 | 52.13 | 51.91 | 51.60 | 48.68 lf) |
| 8 | 61.28 | 59.55 | 59.30 | 57.68 | 57.46 | 57.17 | 52.96 (lf) |
Eigenfrequencies for different models in case of clamped-free support (C-F) [Hz].
| Mode number | Paper | Paper | Paper |
|---|---|---|---|
| 1 | 2.19 | 2.20 | 2.21 |
| 2 | 7.68 | 7.68 | 7.60 |
| 3 | 12.96 | 12.97 | 13.36 |
| 4 | 13.88 | 13.89 | 13.88 |
| 5 | 23.18 | 23.21 | 22.44 |
| 6 | 32.68 | 32.71 | 33.91 |
| 7 | 50.31 | 50.37 | 48.72 |
| 8 | 59.55 | 59.61 | 61.33 |
Eigenfrequencies for different models in case of clamped-clamped support (C-C) [Hz].
| Mode number | Paper | Paper | Paper |
|---|---|---|---|
| 1 | 10.15 | 10.16 | 9.99 |
| 2 | 18.39 | 18.41 | 18.63 |
| 3 | 26.68 | 26.71 | 26.55 |
| 4 | 48.70 | 48.76 | 48.21 |
| 5 | 50.72 | 50.78 | 51.45 |
| 6 | 52.92 | 52.97 | 52.92 |
| 7 | 82.42 | 82.52 | 81.84 |
| 8 | 93.59 | 93.70 | 94.47 |