A Fluidelastic Model for the Nonlinear Dynamics of Two-Dimensional Inverted Flags
Bibliographic record
Abstract
Abstract A nonlinear fluid-elastic model is proposed for the study of the dynamics of inverted flags. The quasi-steady version of Theodorsen’s unsteady aerodynamic theory is used for inviscid fluid-dynamic modelling of the deforming flag in axial flow. Polhamus’s leading edge suction analogy is employed to model flow separation effects from the free end at moderate angles of attack via a nonlinear vortex-lift force. The flag is modelled structurally via a geometrically-exact Euler-Bernoulli beam theory. Using the extended Hamilton’s principle, the nonlinear partial-integro-differential equation governing the dynamics of the inverted flag in terms of the angle of rotation of the flag is obtained. The equation of motion is discretised spatially via the Galerkin method and is integrated in time via Gear’s backward differentiation formula. The bifurcation diagrams are obtained using a time-integration method and pseudo-arclength continuation. It is shown that inverted flags undergo multiple bifurcations with respect to flow velocity, and they generally exhibit four dynamical states: (i) stretched-straight, (ii) buckled, (iii) deflected-flapping, and (iv) large-amplitude flapping. Also, flapping of inverted flags probably develops through fluid-elastic instabilities. Our findings suggest that the system dynamics is sensitive to the mass ratio. It is shown that the mass ratio parameter does not affect the stability of the stretched-straight state and the onset of divergence; however, it controls the possibility of a direct transition from static undeflected equilibrium to large-amplitude flapping motion and it affects the amplitude of large-amplitude flapping.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".