Research Article
Transfer Matrix Method for the Determination of the Natural Vibration Characteristics of Realistic Thrusting Launch Vehicle—Part I
Table 4
First three frequencies (rad/sec) of high and low aspect ratio for a multistage launch vehicle: comparison between [
5] and TMM.
| Mode | Timoshenko beam | Euler-Bernoulli beam | With rotary inertia and shear deformation | With rotary inertia only | With shear deformation only | (without rotary inertia and shear deformation) | Reference [5] | TMM | Reference [5] | TMM | Reference [5] | TMM | Reference [5] | TMM |
| Whole multistage launch vehicle () |
| 1 | 16.017 | 16.005 | 16.054 | 16.042 | 16.083 | 16.069 | 16.120 | 16.107 | 2 | 46.521 | 46.492 | 47.195 | 47.172 | 46.770 | 46.735 | 47.457 | 47.428 | 3 | 93.943 | 93.710 | 97.566 | 97.393 | 94.727 | 94.471 | 98.686 | 98.322 |
| Upper stage of the launch vehicle () |
| 1 | 334.776 | 335.019 | 400.968 | 401.468 | 348.945 | 349.146 | 438.557 | 439.003 | 2 | 760.445 | 760.596 | 1104.970 | 1106.305 | 803.663 | 803.364 | 1367.317 | 1369.986 | 3 | 960.819 | 959.593 | 1655.463 | 1659.978 | 1049.897 | 1048.378 | 2292.381 | 2290.001 |
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