Response and instability prediction of helicopter dynamics on the ground

In helicopters with hinged blades an unstable dynamical phenomenon known as ground resonance may occur during take-off and landing and lead to the total destruction of the aircraft. Predicting the phenomenon is necessary to determine the stability of periodical equations of motion. The instability boundaries can be easily obtained for isotropic rotor configurations through multi-blade coordinate transformation once the periodic terms are eliminated. However, Floquet׳s theory is commonly used to treat the periodic motion equations when introducing the asymmetric effects of spring or damper aging or rotor rupture (anisotropic rotors). In additional, it is known that when treated as parametric excitations, periodic terms may lead to instability in dynamical systems under parametric resonances. In this paper a helicopter in contact with the ground is considered as a parametrically excited system and the equations are treated analytically by applying the method of multiple scales (MMS). A stability analysis verifies the existence of parametric instabilities by first order sets of equations for an isotropic rotor configuration. The results are compared and validated with those obtained by using Floquet׳s Theory. Moreover, the amplitude responses of the aircraft at equilibrium in the remaining resonant cases are studied. The results are then compared with those obtained from the time response analysis.