General Approach to Dynamic Analysis of Rotorcraft

Abstract

This paper presents a general‐purpose mathematical formulation for the dynamic analysis of a rotorcraft consisting of flexible or rigid components, or both, that may undergo large rotations. In this formulation, two sets of coordinates are used, namely rigid‐body coordinates and elastic coordinates. The rigid‐body coordinates define the location and the orientation of a body frame with respect to an inertial frame. The rigid‐body rotational coordinates may be Euler angles, Euler‐like angles, or Euler parameters. The elastic coordinates define the elastic deformations with respect to the body frame. Nonlinear strain‐displacement relations are considered in order to be able to incorporate the effect of geometric stiffening. A systematic methodology that combines the traditional finite element and multibody approaches is developed to obtain a set of differential and algebraic equations governing the dynamics of the system. The resulting set of equations is highly nonlinear. Numerical schemes to solve this set of equations are also discussed. The formulation presented is general and allows the development of a modular code. The formulation also allows the code to be updated and grow without reformulation of the problem.