Nonlinear normal modes of a rotating helicopter blade

Christophe PIERRE
Dean, Faculty of Engineering,
Canada Research Chair in Structural Dynamics and Vibration,
McGill University, Montréal, Québec
Dongying JIANG
MKP Structural Deign Associates, Inc., Ann Arbor, Michigan, USA
Steve SHAW
Department of Mechanical Engineering,
Michigan State University, East Lansing, USA

This research aims at the implementation of new model reduction methods for a nonlinear rotating blade system, based on a nonlinear modal analysis methodology. Invariant manifolds in the systems phase space are used to define nonlinear normal modes of motion for the nonlinear vibratory blade system. A numerical Galerkin technique is utilized to solve for the invariant manifolds, which allows one to construct nonlinear normal modes and carry out nonlinear mode based model reduction for motions in strongly nonlinear regions of the phase space.
This method seamlessly interfaces with the finite element model (FEM) of a prototype of an active twist rotor (ATR) rotorcraft blade, which features significant nonlinear behavior due to rotation, large deformation, and complex blade geometry and materials. The nonlinear normal mode corresponding to the first-order bending motion of the ATR blade is successfully constructed, and a single-DOF reduced-order model is obtained from the corresponding invariant manifold. This reduced-order model accurately and efficiently represents the nonlinear dynamics of the ATR blade in its first-order bending mode.
Numerical time simulations on the invariant manifold show that the lead-lag and axial elongation motions are essential in capturing the bending-dominated blade motion accurately. Due to the generality of the proposed methodology, the invariant-manifold-based model reduction methodology can be conveniently extended to more complete rotating blade models, including those with aerodynamic coupling.

Laboratoire de Mécanique des Structures et des Systèmes Couplés - LMSSC