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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.

IntroductionThe complex dynamics of the coronavirus disease 2019 (COVID-19) pandemic has made obtaining reliable long-term forecasts of the disease progression difficult. Simple mechanistic models with deterministic parameters are useful for short-term predictions but have ultimately been unsuccessful in extrapolating the trajectory of the pandemic because of unmodelled dynamics and the unrealistic level of certainty that is assumed in the predictions.Methods and analysisWe propose a 22-compartment epidemiological model that includes compartments not previously considered concurrently, to account for the effects of vaccination, asymptomatic individuals, inadequate access to hospital care, post-acute COVID-19 and recovery with long-term health complications. Additionally, new connections between compartments introduce new dynamics to the system and provide a framework to study the sensitivity of model outputs to several concurrent effects, including temporary immunity, vaccination rate and vaccine effectiveness. Subject to data availability for a given region, we discuss a means by which population demographics (age, comorbidity, socioeconomic status, sex and geographical location) and clinically relevant information (different variants, different vaccines) can be incorporated within the 22-compartment framework. Considering a probabilistic interpretation of the parameters allows the model’s predictions to reflect the current state of uncertainty about the model parameters and model states. We propose the use of a sparse Bayesian learning algorithm for parameter calibration and model selection. This methodology considers a combination of prescribed parameter prior distributions for parameters that are known to be essential to the modelled dynamics and automatic relevance determination priors for parameters whose relevance is questionable. This is useful as it helps prevent overfitting the available epidemiological data when calibrating the parameters of the proposed model. Population-level administrative health data will serve as partial observations of the model states.Ethics and disseminationApproved by Carleton University’s Research Ethics Board-B (clearance ID: 114596). Results will be made available through future publication.

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