Application of Floquet Theory to Helicopter Blade Flapping Stability.
Abstract
The purpose of this thesis was to explore the flapping stability of a helicopter rotor blade in forward flight. The equations of motion for the flapping motion for the flapping motion of the blade were converted from nonlinear differential equations with periodic coefficients to linear periodic differential equations through the assumption of a rigid blade where the elastic flapping deflections are negligible as compared to the rigid body flapping rotations about the flapping hinge. Aeroelastic effects were not considered. The stability of the homogenous part of the flapping motion linearized periodic differential equations was examine through the application of Floquet theory. The flapping blade motion was simulated over one period to derive the elements of the monodromy matrix. The monodromy matrix was next transformed into Jordan normal form through a similarity transformation to obtain its characteristic values and eigenvectors. The characteristic values were converted to their respected Poincare' exponents and the periodic eigenvectors composition was determined and transformed into Fourier series representations. A feedback controller was constructed using Floquet theory for the unstable blade flapping motion case. Keywords: Fourier series; Numerical integration; and Control theory.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1984
- Accession Number
- ADA154460
Entities
People
- J. K. March
Organizations
- Air Force Institute of Technology