Mathematical Problems in Engineering / 2013 / Article / Tab 4

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.

ModeTimoshenko beamEuler-Bernoulli beam
With rotary inertia and shear deformationWith rotary inertia onlyWith shear deformation only(without rotary inertia and shear deformation)
Reference [5]TMMReference [5]TMMReference [5]TMMReference [5]TMM

Whole multistage launch vehicle ( )

116.01716.00516.05416.04216.08316.06916.12016.107
246.52146.49247.19547.17246.77046.73547.45747.428
393.94393.71097.56697.39394.72794.47198.68698.322

Upper stage of the launch vehicle ( )

1334.776335.019400.968401.468348.945349.146438.557439.003
2760.445760.5961104.9701106.305803.663803.3641367.3171369.986
3960.819959.5931655.4631659.9781049.8971048.3782292.3812290.001