Analysis of steady-state response regimes of a helicopter ground resonance model including a nonlinear energy sink attachment

Baptiste Bergeot (1) , Sergio Bellizzi (2) , Bruno Cochelin (1)

1 M&S - Matériaux et Structures
2 Sons

Helicopter Ground Resonance (GR) is a dynamic instability involving the coupling of the blades motion in the rotational plane (i.e. the lag motion) and the motion of the fuselage. This paper presents a study of the ability of a Nonlinear Energy Sink (NES) to control a GR. A model of helicopter having a minimum number of degrees of freedom and being able to reproduce GR instability is obtained using successively Coleman transformation and binormal transformation. A theoretical/numerical analysis of the steady-state responses of this model is performed when a NES is attached on the fuselage in an ungrounded configuration. The analytic approach is based on complexification-averaging method together with geometric singular perturbation theory. Four steady-state responses are highlighted and explained analytically: complete suppression, partial suppression through strongly modulated response, partial suppression through periodic response and no suppression of the GR. A systematic method based on simple analytical criterions is proposed to predict these steady-state response regimes. The method is finally validated numerically.

Mots clés: Strongly modulated response; Relaxation oscillations; Passive control; Non linear energy sink; Helicopter ground resonance

Domaines: Dynamique Chaotique [nlin.CD]; Vibrations [physics.class-ph]; Acoustique [physics.class-ph]

Baptiste Bergeot, Sergio Bellizzi, Bruno Cochelin. Analysis of steady-state response regimes of a helicopter ground resonance model including a nonlinear energy sink attachment. 2014. ⟨hal-01091763v1⟩