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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

On the Stability of a Rotating Blade with Geometric Nonlinearity

Journal of Applied Nonlinear Dynamics 1(3) (2012) 263--286 | DOI:10.5890/JAND.2012.06.002

Fengxia Wang; Albert C.J. Luo

Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, Edwardsville, IL62026-1805, USA

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Abstract

The stability of a rotating, nonlinear blade under a time-varying torque is investigated. The nonlinear blade is presented based on the geometric nonlinearity.Compared to the nonlinear model, the linear model of a rotating blade with effective load is investigated. The two models of rotating blades are reduced to the ordinary differential equations through the Galerkin method, and gyroscopic systems with parametric excitations are obtained. From such gyroscope systems, the stability of the two models is studied by the generalized harmonic balance method, and the approximate, analytical solutions for the two models are obtained. The stability regions in parameter maps are presented for a better understanding of the stability of such parametric, time-varying systems. The analytical and numerical solutions are illustrated. This study provides an efficient and accurate way to determine the stability of gyroscope systems with time-varying excitations.

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