Analytical Responses of Rotor–Nacelle Systems Subjected to Nonwhite Aerodynamic Moments

Tilt-rotor aircraft may be subjected to long-correlated random loads in their complex flight environments, potentially inducing dynamics distinct from those based on deterministic force or idealized white-noise assumptions in existing studies. In this paper, we explore the whirl flutter of tilt-rotor aircraft subjected to nonwhite random aerodynamic moments, modeled as two-degree-of-freedom nonlinear rotor–nacelle systems with fractional Gaussian noise. Firstly, a harmonic balance method is employed to obtain the amplitude response characteristics of the deterministic rotor–nacelle systems. Subsequently, a dimensionality reduction approach based on diffusion approximation theory is proposed for the analysis of stochastic rotor–nacelle systems. To achieve a precise and efficient calculation of system responses, a memory-dependent Fokker–Planck–Kolmogorov equation method is further introduced. Finally, numerical simulations are conducted to verify the effectiveness of the proposed solution methodology. In addition, the statistical characteristics of the responses of stochastic rotor–nacelle systems are examined in detail, and the influence of system parameters on the responses is systematically studied. We discover that the second-order central moments of the system responses increase with the decrease of the Hurst index of the FGN, while they increase with the increase of the freestream-to-blade-tip velocity ratio, the rotor angular velocity, and the noise intensity. The results reveal that both structural and noise parameters have significant impacts on the dynamic stability of the systems, further threatening the safety of tilt-rotor aircraft.