Aeroelastic oscillations of a pitching cantilever wing with structural geometric nonlinearities: theory, numerical simulation and global sensitivity analysis
Bibliographic record
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 T x Moment about the x-axis due to longitudinal stress P x Moment about the x-axis due to warping M y Moment about the y-axis M z Moment about the z-axis Displacements u(x, t) Axial displacement of the elastic axis in the x direction v(x, t) Edgewise (in-plane) bending displacement of the elastic axis in the y direction w(x, t) Flapwise (out-of-plane) bending displacement of the elastic axis in the z direction φ(x, t) Flexible twist displacement measuring the rotation of the cross section about the x-axis θ(t) Rigid body pitch rotation measuring the rotation about the X-axis V(X , T ) Nondimensional edgewise bending displacement W(X , T ) Nondimensional flapwise (out-of-plane) bending displacement ϕ(X , T ) Nondimensional flexible twist displacement ϑ(T ) Nondimensional rigid body pitch rotation Cross-sectional properties EA Axial stiffness EI y Bending stiffness for bending about the y-axis EI z Bending stiffness for bending about the z-axis GJ Torsional stiffness for twisting about the x-axis K θ Stiffness of the torsional spring at the base of the wing m Mass of the wing per unit length Ī0 Mass moment of inertia of the wing about the elastic axis per unit length I θ Mass moment of inertia of the support mechanism at the base of the wing about the pitch axis D θ Structural damping coefficient in the pitch degree of freedom e Distance from elastic axis to mass centroid (positive when center of gravity is ahead of elastic axis) e p Distance from elastic axis to pitch axis (positive when pitch axis is aft of elastic axis) xiii e A Distance from elastic axis to area centroid (positive when tensile axis is ahead of elastic axis) e c Distance from elastic axis to the aerodynamic center (positive when aerodynamic center is ahead of elastic axis) 1 Nondimensional axial stiffness
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".