Random dynamics of a structurally nonlinear airfoil in turbulent flow

The main objective of this thesis is to investigate the effects of turbulent flow on the random dynamics of structurally nonlinear airfoil. A secondary objective is to articulate a more comprehensive picture of the contribution of the longitudinal component of turbulence, as experienced by the airfoil, be it linear or nonlinear. In this regard, a systematic and detailed numerical analysis of the airfoil experiencing random flutter/Hopf bifurcation is presented. Some aspects of the divergence/pitchfork problem are also discussed.The airfoil is modelled as a flexibly mounted rigid flat plate with degrees-of-freedom in pitch and heave. The principal nonlinearity considered is a hardening cubic torsional spring. The aerodynamics is incompressible and linear. Unsteady aerodynamic effects due to arbitrary motion and turbulence are modelled. Both longitudinal and vertical components of the Gaussian turbulence are considered. Longitudinal turbulence acts as a parametric excitation, whereas the latter represents an external forcing.A Monte Carlo simulation is performed to solve numerically the system of random differential equations. The time history solutions are then studied in terms of their mean-square, probability density function and power spectral density. The largest Lyapunov exponent is also calculated.The bifurcation, stability and response characteristics of the airfoil are examined. For the linear airfoil, it is found that the coalescence flutter speed is always advanced by the longitudinal component of turbulence, and generally dominated by the very low frequency range of the excitation. Divergence can be either advanced or postponed, but the magnitude of the shift is not significant compared with flutter. Furthermore, it is shown that in general longitudinal turbulence decreases the overall stability of the airfoil, be it linear or nonlinear.For the nonlinear airfoil, it is the vertical component of turbulence that determines the essential features of the stochastic bifurcation and the qualitative characteristics of the response. The interplay between turbulence and nonlinear stiffness has a significant impact on the probability structure of the aeroelastic response. Uni-, bi- and double bi-modal distributions are observed, and found to occur at different airspeeds depending on which state variable is considered. Furthermore, the spectral content displays noise-controlled, and noise-induced, time scales