Eur. Phys. J. Special Topics 222, 1707-1731 (2013)
https://doi.org/10.1140/epjst/e2013-01957-1

Regular Article

Analytical periodic motions in a parametrically excited, nonlinear rotating blade

Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, Edwardsville, IL 62026-1805, USA

^a e-mail: fwang@siue.edu
^b e-mail: aluo@siue.edu

Received: 4 June 2013
Revised: 2 August 2013
Published online: 30 September 2013

Abstract

The stability and bifurcation analyses of periodic motions in a rotating blade subject to a torsional excitation are investigated. For high speed rotations, cubic geometric nonlinearity and gyroscopic effects of the rotating blade are considered. From the Galerkin method, the partial differential equation of the nonlinear rotating blade is simplified to the ordinary differential equations, and 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. The rich dynamics and co-existing periodic solutions of the nonlinear rotating blades are investigated.