Non-linear flap-lag dynamics of hingeless helicopter blades in hover and in forward flight

The aeroelastic instability of the coupled non-linear flap-lag motion of a torsionally rigid helicopter blade is treated by using the perturbation method in multiple time scales. The non-linearities present in the equations are those arising from the inclusion of moderately large deflections in the inertia and aerodynamic loading terms. The stability boundaries, amplitudes of non-linear response and conditions for existence of limit cycles are obtained analytically. Thus, the different roles played by the forcing, parametric excitation and non-linear coupling in affecting the solution can be easily identified. Numerical results illustrating the behaviour of the blade are presented.