en:example:dyn:1:start
Table of Contents
Natural frequencies
by Dr. Jiří Plešek
Problem description
Calculate the lowest ten natural frequencies of the cantilever beam shown. Compare the FEM results with the theoretical beam solution.
Material properties
$E=2\times10^5\text{ MPa},$ $\nu=0.3,$ $\rho=7800\text{ kg/m$^3.$}$
Solution
The results of the computation are shown in the table below.
| # | $f\text{ [Hz]}$ | mode | ||||
|---|---|---|---|---|---|---|
| theory | BEAM56 | BEAM61 | BEAM53 | BEAM71 | ||
| 1. | $8.18$ | $8.55$ | $8.18$ | $8.18$ | $8.45$ | bending |
| 2. | $16.36$ | $16.93$ | $16.36$ | $16.36$ | $16.85$ | bending |
| 3. | $51.26$ | $58.04$ | $51.32$ | $51.32$ | $55.00$ | bending |
| 4. | $102.53$ | $113.84$ | $112.65$ | $102.65$ | $112.03$ | bending |
| 5. | $143.54$ | $190.36$ | $147.91$ | $144.65$ | $174.56$ | bending |
| 6. | $365.61$ | $312.76$ | $285.36$ | $354.23$ | ||
| 7. | $287.08$ | $491.76$ | $360.57$ | $289.30$ | $422.37$ | bending |
| 8. | $636.44$ | $552.92$ | $530.75$ | $662.06$ | ||
| 9. | $940.21$ | $706.11$ | $570.72$ | $826.68$ | ||
| 10. | $702.21$ | $1277.15$ | $928.46$ | $706.73$ | $914.59$ | torsion |
en/example/dyn/1/start.txt · Last modified: 2022-02-11 14:25 by Petr Pařík