VIBRATION AND BUCKLING OF FLEXIBLE ROTATING BEAMS

Perturbation techniques are employed to estimate the free vibration ch aracteristics and buckling limit of a flexible rotating Bernoulli-Eule r beam. The normalized beam stiffness epsilon = EI/m Omega(2) (R) over bar(4) is introduced and treated as a small parameter, Then, singular perturbation solutions to the governing eigenvalue problem are derive d that are valid up to and including order epsilon for any given hub r adius. The special case of a zero hub radius is then considered and th e corresponding solutions are presented. Next, a transformation is int roduced which leads to a regular perturbation formulation of the probl em the solution of which is presented. The natural frequency/mode shap e predictions and buckling limits obtained from both the singular and regular perturbation formulations are compared with ''exact'' values o btained from a power series solution of the eigenvalue problem. The si ngular perturbation solution matches well with the ''exact'' values fo r small stiffnesses whereas the regular perturbation solution provides an excellent accuracy for all beam stiffnesses and hub radii consider ed.