The Dynamics of Helicopters with Nonlinearities on the Fuselage
Leonardo Sanches  1@  , Cesar Augusto Borges Da Silva  2  , Guilhem Michon  3  
1 : Université de Toulouse
2 : Federal University of Uberlândia, School of Mechanical Engineering, Uberlandia - MG, Brazil
3 : Université de Toulouse
ICA, CNRS, ISAE-Supaero, Toulouse, France

Concerning the helicopter dynamics, one aims to avoid the increment of vibrations in every possible operating conditions. Despite the dynamical characteristics of the mechanical components, the interaction of the helicopter with the terrain during starts and landings can cause multiples resonances which might lead to ground resonance with fatal consequences. Depending on the soil characteristics, the interactions with the terrain might lead up to nonlinear behaviours.

Moreover, in order to suppress the ground resonance, elastomeric dampers can play a significant role in the stability of the aircraft. Therefore, the modeling of the elastomeric lag dampers have received increasing attention, specially concerning its nonlinear characteristics. For example, Gandhi and Chopra place an additional nonlinear spring in series with the linear, parallel spring and dashpot in order to represent the elastomeric dampers.

Nevertheless, it is known from the literature that rotating machines under nonlinear operating characteristics could attain other than the periodic motion, predicted for linear systems, the quasi-periodic or chaotic motions.

Recently, Varney and Green observed the presence of quasi-periodic and chaos on the rotor dynamics by assuming rotor-stator contact. Indeed this phenomenon is observed since precisely manufactured bearings are used and thus reduced clearances are imposed for improving the performance of the rotating machines.

Under the hypothesis of nonlinearities presented on the ground resonance modelling, this paper aims verifying, if at certain operating conditions or design properties, the appearance of chaotic motion is reached. The helicopter considered contains nonlinear spring stiffness on the fuselage displacements (longitudinal and lateral). The four-bladed rotor consider rigid structures having only lead-lag oscillations. Parametric analyses combined with examination of the Poincare maps and bifurcation diagrams, the nonlinear dynamical behavior of the helicopter was assessed. Non-periodic motion is attained for several rotor speed values and helicopter configuration analyzed.

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