On the Dynamics of a Helicopter Rotor Blade
by
M. R. M. Crespo da Silva
Department of Mechanical Engineering, Aeronautical Engineering and Mechanics; Rensselaer Polytechnic Institute, Troy, NY 12180-3590

As in practically all dynamical systems, the differential equations that govern the flap-lag-torsional dynamics of heliciopter rotor blades are strongly nonlinear. The nonlinearities are due to the elastic deformation of the rotor blade (even if the blade's material is linearly elastic), and to the nonlinear dependence of the generalized aerodynamic forces on the elastic deformations of the blade. It has been a common practice in the rotorcraft dynamics literature to expand the nonlinearities in such equations in Taylor series about the undeformed state of the blade and then analyze the motion using a set of eigenfunctions for a nonrotating beam. Besides being approximate, this procedure yields a very large number of equations for one to deal with.

A mathematically rigorous analysis of the response of a helicopter rotor blade in hover is presented in this paper. First, the formulation of the nonlinear partial differential equations of motion is presented. The equilibrium solution exhibited by the system is then determined numerically by solving the nonlinear two-point boundary value problem that results from such equations. The equilibrium solution is then perturbed and the stability of infinitesimally small perturbations is analyzed in detail in a mathematically exact manner. The many possibilities for the occurrence of nonlinear resonances in the system and further work involving the effect of the nonlinearities in the dynamic response are also discussed.

Date received: January 12, 1998

Copyright © 1998 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caav-03.