Module 10 : Finite Element Analysis of Rotors with Gyroscopic Effects

Lecture 1 : Timoshenko Beam Theory

 

For the present case R is less than 0.02 so effect of shear is less but as rotary inertia is also considered, natural whirl frequencies of the rotor bearing system decreases as compared to Euler-Bernoulli case. This decrease is 0.3%, 1.8%, 2% and 3% for the first, second third and fourth modes, respectively. The difference is higher at higher modes since the rotary inertia becomes predominant at higher frequencies. It should be noted that in the present problem, the rotor is assumed to be non-rotating and because of this gyroscopic couple is absent. The case of rotating shaft with the rotary inertia, shear deformation and gyroscopic couple would be considered in the next section.