Research Article
Structural Damping Effects on Dynamic Instability of Subtangentially Loaded and Shear Deformable Beck’s Columns
Table 6
Divergence and damped flutter loads of Beck’s columns for
, 0.005, and 0.02 with variation of
.
| Subtangentiality, α | 0.0 | 0.1 | 0.2 | 0.3 | 0.321 | 0.354 | 0.4 | 0.439 | 0.5 | 0.6 | 0.7 | 0.8 | 0.9 | 1.0 | 0.317† | 0.352† | 0.433† | 0.488† | 0.306‡ | 0.345‡ | 0.413‡ | 0.456‡ |
| Undamped second flutter load, | — | — | — | — | 19.42 | 24.13 | 28.78 | 33.34 | 49.35 | — | — | — | — | — | 17.68† | 22.41† | 27.35† | 31.78† | — | 13.96‡ | 18.81‡ | — | — | — |
| Undamped first flutter load, (= externally damped flutter load, ) | — | — | — | — | 19.42 | 17.08 | 16.40 | 16.16 | 16.05 | 16.26 | 16.79 | 17.59 | 18.67 | 20.05 | 17.68† | 15.39† | 14.73† | 14.52† | 14.37† | 14.47† | 14.84† | 15.43† | 16.20† | 17.16† | 13.96‡ | 11.89‡ | 11.29‡ | 11.21‡ | 11.03‡ | 10.94‡ | 11.08‡ | 11.35‡ | 11.70‡ | 12.12‡ |
| 2% damped flutter load, | — | — | — | — | 19.22 | 17.08 | 15.86 | 14.55 | 14.20 | 14.12 | 14.40 | 14.98 | 15.85 | 17.03 | 17.48† | 15.39† | 14.22† | 13.17† | 12.85† | 12.71† | 12.92† | 13.36† | 14.01† | 14.87† | 13.80‡ | 11.89‡ | 10.74‡ | 10.38‡ | 10.12‡ | 9.857‡ | 9.946‡ | 10.17‡ | 10.49‡ | 10.90‡ |
| Internally damped flutter load, | — | — | — | — | 19.42 | 17.08 | 15.86 | 14.55 | 9.870 | 9.379 | 9.305 | 9.529 | 10.05 | 10.94 | 17.48† | 15.39† | 14.22† | 13.17† | 9.237† | 8.719† | 8.657† | 8.855† | 9.303† | 9.983† | 13.96‡ | 11.89‡ | 10.74‡ | 10.35‡ | 7.797‡ | 7.231‡ | 7.194‡ | 7.338‡ | 7.637‡ | 8.083‡ |
| 2nd divergence load, | 22.21 | 21.17 | 19.89 | 18.23 | 17.81 | 17.08 | 15.86 | 14.55 | 9.870 | — | — | — | — | — | 19.99† | 19.05† | 17.90† | 16.40† | 16.09† | 15.39† | 14.22† | 13.17† | 9.237† | 15.38‡ | 14.66‡ | 13.77‡ | 12.59‡ | 12.51‡ | 11.89‡ | 10.74‡ | 10.35‡ | 7.797‡ |
| 1st divergence load, | 2.467 | 2.830 | 3.325 | 4.055 | 4.257 | 4.626 | 5.292 | 6.099 | 9.870 | — | — | — | — | — | 2.437† | 2.795† | 3.286† | 4.012† | 4.174† | 4.560† | 5.263† | 5.952† | 9.237† | 2.351‡ | 2.697‡ | 3.174‡ | 3.891‡ | 3.947‡ | 4.361‡ | 5.204‡ | 5.509‡ | 7.797‡ |
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The unmarked, , and marked values denote critical loads corresponding to , 0.005, and 0.02, respectively.
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