Aeroelastic oscillations of a pitching cantilever wing with structural geometric nonlinearities: theory, numerical simulation and global sensitivity analysis

Abstract

The focus of this thesis is the aeroelastic dynamics of a rectangular cantilever wing with a NACA 0012 profile, whose base is free to rotate rigidly about a longitudinal axis. The wing is analytically modelled as part of a project to simulate the dynamics of an aeroelastic wind tunnel model.Structural geometric nonlinearities are modelled to the second order to capture the essential effects of large deformation. While the derivation closely follows common approaches from the literature on the subject of the nonlinear bending and torsion of rotor blades, this aeroelastic system contains new inertial terms which stem from the fundamentally different kinematics that arise from the added rigid body degree of freedom in pitch. A system of coupled nonlinear partial differential equations (PDEs) and an ordinary differential equation (ODE) is derived using Hamilton's principle. These equations of motion describe the coupled axial-bending-bending-torsion-pitch motion of the system. A Galerkin projection scheme is employed to obtain a finite dimensional representation of the equations of motion, leading to a coupled system of ODEs. The resulting nonlinear ODEs are solved numerically using Houbolt's method. The results that are obtained are verified by comparison with the results obtained by direct integration of the equations of motion using a finite difference scheme. Using unsteady linear aerodynamics, it is observed that the system undergoes coalescence flutter due to coupling between the rigid body pitch rotation dominated mode and the first flapwise bending dominated mode. The post-flutter behaviour is dictated by the structural geometric nonlinear terms which limit the oscillations to a limit cycle. Global sensitivity analysis is performed to study the effect of parametric uncertainty introduced by the rigid body base rotation on the flutter speed and associated frequency. It is found that the stiffness parameter has the largest influence on the variation of both the flutter speed and frequency, while the structural damping has a negligible influence.

Sensitivity Analysis and Experimental Validation of Plunger-type Wavemakers Modelled with a Steady Flow

“…and similarly for higher order terms. The unconditional variance of the output V (Y ) can also be determined by [Rob18],…”

Anomaly Detection in the Vibration of Wind Turbine Blades using Gaussian Process Regression

“…Additionally, C L , C D , C M are the aerodynamic coefficients of lift and drag forces, and pitching moment at the aerodynamic center (AC), respectively. In general, the AC is located at the quarter of chord length from the leading edge in the case of a subsonic flow (which is the type of flow used in this study), as presented in Figure 3.5 [55]. The AC is shifted to half chord point for a supersonic flow [55].…”

“…In general, the AC is located at the quarter of chord length from the leading edge in the case of a subsonic flow (which is the type of flow used in this study), as presented in Figure 3.5 [55]. The AC is shifted to half chord point for a supersonic flow [55]. By definition, the aerodynamic moment is independent of the angle of attack at the AC, and is equal to 0 for symmetrical airfoils under a subsonic flow [50].…”