Analytical vibrations of a rotating blade with geometric nonlinearity

Analytical vibrations and stability of a rotating blade subject to a torsional excitation are investigated. A model with cubic geometric nonlinearity and gyroscopic effects is presented. From the Galerkin method, the partial differential equation of the nonlinear rotating blade is reduced. Further, periodic motions and stability of the rotating blade are studied by the generalized harmonic balance method. The analytical and numerical results of periodic solutions are compared. From such initial investigation, the rich dynamics and co-existing periodic solutions of the nonlinear rotating blades should be further investigated.