Non-linear simulation of coupled rotor-fuselage response using symbolically derived equations of motion. Part 1: Derivation

Abstract

This paper presents a new simulation method for ground and air resonance stability analysis of helicopter rotor systems. The method presented is based on the formulation of the full non-linear equations of motion of three rigid offset blades with degrees of freedom in the¯ap and lead/lag and a hub that has two translational degrees of freedom for the body. The set of non-linear equations of motion is developed by the Lagrangian method using symbolic processing software for expanding the equations. In addition, the symbolic software automatically converts the equations of motion into a source code that is optimized for numerical integration. Part 1 of this paper addresses the derivation of the equations of motion for the rotor±body combination. Part 2 of this paper addresses the comparison of simulation output to referenced works and includes several unique applications that take advantage of the non-linear capability of the resulting simulation.

Parametrically excited helicopter ground resonance dynamics with high blade asymmetries

“…The effects of geometric nonlinearities and the use of nonlinear springs on the prediction of instabilities was verified [14,15] with the application of perturbation methods. Moreover, the dynamics of a helicopter subject to ground resonance, taking into account blade dissimilarities was examinated [16].…”

Aplicação do Nonlinear Energy Sink (NES) no controle passivo da instabilidade em helicóptero com anisotropia

“…Donham et al (1969) reformularam as equações do movimento considerando os efeitos aerodinâmicos e visando identificar as instabilidades devido a dois tipos de ressonância: ar e solo. Além destes autores, Lytwyn et al (1971) Robinson et al (1998Robinson et al ( , 2004a; Flowers e Tongue (1988); Janowski e Tongue (1988); Kunz (2000). Em alguns destes trabalhos já se identifica que os métodos de pertubação foram usados para capturar os efeitos da não linearidade na dinâmica do sistema.…”