Helicopter Ground Resonance 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 capacity of a Nonlinear Energy Sink to control a Helicopter Ground Resonance. A model of helicopter with a minimum number of degrees of freedom that can reproduce Helicopter Ground Resonance instability is obtained using successively Coleman transformation and binormal transformation. A theoretical/numerical analysis of the steadystate responses of this model when a Nonlinear Energy Sink is attached on the fuselage in an ungrounded con guration is performed. The analytic approach is based on complexi cationaveraging 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 Helicopter Ground Resonance. A systematic method based on simple analytical criterions is proposed to predict the steady-state response regimes. The method is nally validated numerically.
10 Figures and Tables
Figure 1: Descriptive diagram of the used helicopter system. (a) Overview of the system. (b) View from the top.
Table 1: Values of λδ and a used in Examples 1, 2a, 2b, 3a, 3b, 4a and 4b. Coordinates N e1 , N e 2 and N e 3 of the corresponding xed points of (68) are also indicated. S ≡ stable and U ≡ unstable.
Figure 3: Descriptive diagram of the used helicopter system coupled to an ungrounded NES. View from the top.
Figure 5: Critical Manifold (CM). Following parameters are used: ωy = 1, α3 = 2 and µ = 0.2. (a) In the (N1,N2)-plan and (b) In the (N1,N2,N3)-space.
Figure 8: λδ,wn and λδ,won as a function of a. Parameters used: see Eq. (85).
Figure 9: Algorithm for the determination of the domain of existence of the steady-state regimes of the SHM+NES (34). Each domain is described precisely in Sects. 5.1 to 5.4.
Figure 14: Example 3a. Parameters used: see Eq. (85), a = 0.4 and λδ = 0.2. Same caption as for Fig. 11.
Figure 15: Example 3b. Parameters used: see Eq. (85), a = −0.4 and λδ = 0.2. Same caption as for Fig. 11.
Figure 16: Example 4a. Parameters used: see Eq. (85), a = −0.7 and λδ = 0.1. Same caption as for Fig. 11.
Figure 17: Example 4b. Parameters used: see Eq. (85), a = −0.4 and λδ = 0.035. Same caption as for Fig. 11.
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