5.4.5.4. Bending vibration of rotor model

Figure 5.26 A rotating blade

RecurDyn allows performing the eigenvalue analysis in time domain. The system characteristics of a rotating blade differ from those of the blade in a static state due to the geometric stiffening effect.

The rotating blade shown in Figure 5.26 is modeled with 21 lumped masses, 20 beam force elements and one revolute joint. The material properties of the rotor are shown in Table 5.9.

Table 5.9 The material properties and geometric entity conditions of rotor

Length	6800 m
Mass	200 Kg
Young’s modulus	7x108 N/mm2
Inertia of area	4 x 105 mm4
Shear modulus	6 x 108 mm4
Area	2000 mm2
Damping ratio	0.0

The following driving constraint is imposed on the revolute joint:

\(^D \mathbf{\Phi}(q,t)=\theta-50t^2=0\)

The natural frequencies of the rotor as the speed increases are shown in Figure 5.27. As the angular speed increases, the natural frequencies of each mode become large. The eigenvalue changes are very similar these in literatures.

Figure 5.27 The angular speed and eigenvalue change