Response probability structure of a structurally nonlinear fluttering airfoil in turbulent flow

The stationary probability structure for the aeroelastic response of a structurally nonlinear fluttering airfoil subject to random turbulent flow is examined numerically. The airfoil is modelled as a two-dimensional flat plate with degrees of freedom in torsion and heave (vertical displacement). The nonlinearity is a hardening cubic stiffness force in the torsional direction. The aerodynamic force and moment are assumed to be linear, thus limiting the analysis to small oscillations; unsteady effects are retained. Furthermore, both parametric and external random coloured excitations are considered. It is found that depending on the value of turbulence variance and nonlinear cubic stiffness coefficient, the pitch marginal probability density functions (PDF) exhibits uni-, bi- or double bi-modality; the nature of the bi-modality is not unique. An explanation of the behaviour is provided via an analysis of the joint PDF in pitch and pitch rate for which both the deterministic and random responses are examined. More generally, it is found that the random excitation effectively ‘decouples’ the nonlinear responses such that the pitch, pitch rate, heave and heave rate marginal PDFs transition from uni- to bi-modality at different airspeeds. It is argued that a fundamental cause of the observed behaviour is the synergy between the nonlinearity and the random external excitation.